I would like to argue that it is not appropriate to close a question as a duplicate based on an answer to another question. A question should only be closed as a duplicate when the same question already exists. There are several reasons for this.
When a question is closed as a duplicate a link gets added to it which directs you to the other post. However, that link is to the other question, not to any answers to the question. If someone has a question and gets sent to a different question (where the overlap is not readily apparent) to find the answer, confusion is likely to ensue upon reading the question and finding it to be a different question.
Where's the Answer?
Closely related to the previous point is the fact that there is no indication where the answer to your question is to be found on the other question. Even if you get past the question without giving up upon seeing a different question, you now have to search for the answer. Sometimes it will be obvious. The answer to your question will clearly jump out at you right in the top answer post. But sometimes it won't be obvious. What if the answer to your question is only a tangential part of the answer to the other question. You might not be able to easily find the sentence or paragraph in the other answer which answers your question, and the more elaborate the other answer is the harder this becomes. Additionally, what if the answer to your question is not contained in the top answer at all? Now you have to sift through multiple answers to a different question, where the majority of the content might be irrelevant for the purpose of answering your question, just to find an answer to your question.
Of course, the closers could leave comments to the closed question with more specific information (e.g. "the third sentence in the fourth paragraph answers your question). However, as this is not required in order to close a question there is nothing to ensure that it is done. In my experience, I have rarely seen such comments or even general comments explaining why a question is a duplicate (unless specifically challenged by other comments). The one example that I recall where a comment pointed to a specific line that rendered a question a duplicate, it turned out that it did not actually answer the new question (more about that later).
Quality of the Answer
Normally when a question is posted and it receives answers there is a pretty good mechanism for determining the quality of the answer. Good answers get upvoted and bad answers get downvoted. This generally ensures (of course it doesn't always work) that the most featured answer to a question is a good answer. However, if a question is closed as a duplicate of an answer to a different question, the quality control mechanism is undermined. Answer X might be a superb answer to Question Y, and have 100 upvotes, but that doesn't mean that the sentence or paragraph contained therein which happens to address Question Z is a good answer to Question Z. The reason why it has 100 upvotes is that it did a good job of addressing Question Y. Even if the part that happens to address Question Z does a bad job of answering Question Z it is unlikely that the answer will get downvoted on that account, since the answer is still a good answer to the question it was posted to answer. Thus, it is possible that by closing the new question we are providing a low quality answer instead of high quality answers.
An extension of this is the fact that if an answer is posted to address one question, the author was likely not putting much (or any) effort into answering a different question. That means that in the event that an answer to one question happens to address another question it is likely to specifically not be a good comprehensive answer to the other question. If it was not the main point of the answer it was included in, the author has no motivation to add an extra few paragraphs to make it a better, more comprehensive, answer to a question that it was not posted to answer.
This leads us to what I think is the most important point. Especially given the nature of the topic of this particular site, many questions do not have a simple objective answer. Many answers involve quite a bit of speculation and extrapolation from vague evidence. There can easily be multiple good answers to a single question, and sometimes even multiple good answers that flat out disagree with each other.
Now on a normal question, any answer that addresses the question can be posted and be subjected to the critical eye of the community via upvotes and downvotes. But when a question is closed as a duplicate of an answer to a different question it creates a problem. The answer to the other question likely only contains one possible answer to the new question. What is supposed to happen to other potential answers to the new question that are significantly different from the answer posted as part of the answer to the old question? They can't be posted to the new question because the new question is closed. They often can't be posted to the old question because they don't address the old question since the old question is actually a different question.
I discussed this particular issue at length in this Meta post. In particular, this answer there showed that an answer that I posted to a question about the total number of students in Hogwarts did not address a different question of whether Hogwarts houses have quotas, and therefore the closure of the former as a duplicate of the latter (because of an answer to the latter which touched upon the total number of students) prevented my answer from being posted at all (until the question was reopened). That, in my opinion, is a bad thing, especially as I think that my answer to the number of students was a pretty good answer (it currently has a score of +14). This example goes straight to the heart of the matter. The answer to the question about quotas dealt with the total number of students in a non-comprehensive manner, and reached a conclusion that is unsupported by a lot of evidence that this answer didn't even mention. This is not necessarily the fault of the answerer, as her goal wasn't to answer the question of total number of students. But this goes to show why it is a bad idea to close a question because an answer to a different question partially deals with it.
The above example was a case where I happened to have a different answer for the closed question. But even without knowing a specific different answer, you can still know that there could be a different answer simply by analyzing how the two questions are different. Of course, if the different answer can also address the open question, it could simply be posted to the open question. But in another answer to that Meta post I showed how you can easily conceive of an answer that would only address one question and not the other, even if you don't have a real answer that fits that criterion. As long as it is theoretically possible to address one without addressing the other the question should not be closed as a duplicate since closing it would prevent the theoretical answers from ever being posted. The general rule that can be used to determine this is:
Would any good answer to one question also address the other question?
That means that as long as it is possible to post a good answer to one question without addressing the other, the questions cannot be considered duplicates.
Reductio Ad Absurdum
Another issue with closing questions as duplicates of answers to different questions is that it can result in some... interesting... conclusions. As I noted in this answer to the above mentioned Meta post almost any question can be made a duplicate of any unrelated answer as long as the unrelated answer throws in one line that states an opinion about the new question. I gave several examples where this happened, and even noted that one could deliberately throw in one-liners assuming a conclusion and thereby close earlier questions that actually asked that very question (and even have good answers).
Another strange result is that if you have a set of three different (but somewhat related) questions, an answer to A can address B and an answer to C can also address B yet these two answers can be different and even contradictory and B can be closed as a duplicate of either one. We can illustrate this with the following example. Here are three different (but related) questions:
In Deathly Hallows, why is Cho Chang still at Hogwarts?
How can Cho Chang be afraid to fail her O.W.L.s if she's a year ahead?
How many Hogwarts students changed year from book to film?
The second of these questions asked why a line in the movie indicates that a character is a year younger than what is indicated in the books. This question is closed as a duplicate of the third question which asks in general about age changes from the books to the movies, and one of the answers there lists this character as someone who's age was altered by the movies. This certainly addresses the question posed in the second question, but it is not necessarily the only answer or the correct answer. Consider that the first of these questions raises a different potential discrepancy about the age of the same character. While one of the answers there shows that the discrepancy is based on a mistaken premise, a different answer (full disclosure: it's my answer) argues that there was never a discrepancy in the first place because the age that everyone assumed for this character based on the books might be incorrect. This answer in turn would address the second question — the reason why a line in the movie makes the character appear to be a year younger is that she actually was a year younger.
So now the second question could be closed as a duplicate of the first question or the third question, which have entirely contradictory answers. One of the answers represents a false fact since the character's age is either one or the other. This means that if any closers only found one of the other two questions they would be closing the second question as a duplicate based on an answer which might be entirely incorrect. And since the first question and the third question are sufficiently different from each other, neither answer can be posted to the other question because it wouldn't address the other question. The proper procedure here should be to leave the second question open, and allow both the answer to the first question and the answer to the third question to be posted to it, and once both contradictory answers exist in the same place they can be pitted against each other and voted upon. Even if the votes don't reach a clear consensus at least any reader can have all the information in one place.
Who Decides if an Answer is Correct?
One might wish to argue that we would only close questions as duplicates of answers to different questions when we know that the answer to the existing question contains the true answer to the new question. If it's just a throwaway line with no evidence then we won't use it to close other questions. However, this would raise an important point. Who gets to decide whether an answer is correct or not? Anyone with 3,000 reputation can cast a close-vote, even if they know nothing about the work in question. They certainly shouldn't be determining whether an answer is correct or not. Users with Gold Badges in the tag for the work in question will hopefully know something about the work but they also should not be determining whether an answer is correct or not. Even "experts" in a given work do not know everything about it; they can easily forget a particular point, or make a mistake. Note that the privileges that come along with increased reputation and Gold Badges are not related to determining the correctness of an answer. The privileges relate to how well you understand the system and how well you can tell whether a question fits into a closeworthy category. No matter how much reputation or privileges a user has he never gets more than one vote on a question or answer itself. That means that when it comes to determining the correctness of an answer, a new user with 125 reputation and a Gold Badge holder with 100,000 reputation are on equal footing. They both get one vote.
This being the case, there is no methodology to use to determine which answers can be used to close other questions and which answers cannot be used. To put it simply, in order to close a question as a duplicate based on an answer to a different question, we would have to presuppose what the answer to the question is. We have no right to do that; in fact the entire point of posting the question is to arrive at the best answers to the question via the mechanism of people posting answers and people voting on the answers posted. Presupposing the answer to the question undermines the system.
An additional issue with closing questions as duplicates based on answers to other questions is that answers can be changed at any time. Usually there won't be such drastic edits, but in many of these cases the part that addresses the new question is not strictly necessary to answer the old question. That makes it much more likely for that part to be removed. If it does get removed the closed question will now link to a question purporting to contain an answer but it will not actually contain an answer.
Another potential negative effect of closing questions as duplicates based on answers is that sometimes there is actually another question that makes it a true duplicate. In such cases, users who are looking for posts to close a question based on might find an answer which addresses the new question, and they might stop searching and just close the new question based on the answer. Had the question not been closed based on an answer, the duplicate search might have continued until an actual duplicate question would be found. It is surely better to have a question linked to and closed as a duplicate of another question which asks the same thing than as a duplicate of a separate question whose answer happens to address the new question as well. I can’t say how often this happens, but here are two recent examples of questions that I found closed as duplicates based on answers to separate questions, and I edited the duplicate list to include questions that actually were asking basically the same thing as the closed question:
Why did the school have a series of difficult, yet doable challenges instead of a spell that keeps people from getting it?
Why could Ronald Weasley use Charlie's old wand?
Why didn't someone make Lily and James Potter portraits like the dead Hogwarts Headmasters?
Why could the pictures and paintings in Hogwarts talk and the photos of Harry's parents couldn't?
Why didn't Malfoy just kill Harry in the Half Blood Prince?
Why didn't the Death Eaters capture Harry Potter at the end of the Half-Blood Prince?
Why didn't the Death Eaters take Harry after Dumbledore's death?
Is it illegal to do magic outside of Hogwarts?