If only one question has a known correct answer, then we should leave the other open.
My response to the suggestion that we close ‘obvious’ story ID dupes has always boiled down to “Okay, but why?”. We have a slightly tidier site, but that seems to be about it. By contrast, there are several reasons not to do it:
If we’re wrong, we’ve just annoyed the OP.
And what have we gained by doing so? The site is slightly tidier, but they don’t have the answer. So we have a frustrated user (who I think is likely to just leave, and not correct us), and bad information on the site.
Even if we’re correct, we’re essentially accepting an answer for the OP.
By asserting that the answer is “obvious” and closing as dupe, we’ve cut the OP out of the process.
There have been many proposals for a mechanism that allows us to accept an answer on somebody else’s behalf, and they’ve always met strong opposition. I don’t see why story identification questions should get special treatment.
At best, we should try to guess what the story is – but only the OP can confirm. We shouldn’t take that control out of their hands.
There are other ways I think we cause harm if we close questions as incorrect dupes, but I don’t have time to write those up at the moment. Suffice to say, I disagree with the idea of closing dupes without OP confirmation.