So if the person asking the question is calling it a duplicate too, why is it still available to reopen?
Initially I was satisfied by the answer given by Masked Man. However, a situation today made me change my mind (still think that this is something that has not been thoroughly analyzed).
Although it makes sense to say "If the one asking the question agrees on a Dupe, then why insist on denying so and ask for reopen?". This makes sense because only OP know what he really is asking or wants.
If that user is satisfied with the dupe why not let it rest there?
Because that user is not the only one on the site, and surely not the only one that could benefit from the post. Maybe the OP just wanted some self-validation, or accepted the dupe in haste because he saw some relatively useful answer over there, or just freaked out and accepted the dupe to put an end to the attention on their question (like the interesting trend of new users to accept the only answer they got on their off-topic, down-voted, and closed post, "just because" or as a "meh, thanks anyway").
As per the post that made me think this over again (yes, I was in the middle of writing an extended and thoughtful answer when it got closed), what worries me is that the user accepted it because he said (quoting) "I believe that question is close enough!" ... close enough?! Although it is subjective, "close enough" is hardly the same a "duplicate".
So, what about all those other users facing the same or similar problem when they find this post just to see it is a Dupe of one that is "close enough"? Will this be also close enough for them? If they are not, they will probably go on and ask such question, but chances are that it will be (again) marked as Dupe of the Dupe of a "close enough" question that someone lightly suggested or that the OP accepted without much consideration. We could continue with this mental experiment, but we can already see it going downhill.
This is why I think that allowing those posts to be reopened helps solve this possible problem, by allowing the Community to determine if such posts are indeed
close enough a duplicate, or if it is worth reopening it as it is of high value for the site and future readers. Maybe the OP got his question partially answered (or settled for such), but this is no reason to limit the answers it may get just because one user is "satisfied" with it.