Okay, since it's been a day I'll post my thoughts for voting.
I think that re-asking a question with a different phrasing is good, provided that the new phrasing removes ambiguity and invalidates the unintended answer. We often have questions which are not specific enough with their initial phrasing. (Mostly [enigmatic-puzzle] and [riddle]). Usually, the OP will just say "nope, not what I was looking for" and leave it at that.
This is discouraging, especially if the answer works well for the given puzzle. It's also an indicator of a lower-quality puzzle. By re-posting with significantly modified phrasing, the puzzle can be improved to remove the loopholes that allowed for an unintended answer. The unintended answer can be accepted because it answers the puzzle as initially presented.
To summarize: I think that re-asking a rephrased puzzle should be encouraged because
- It allows the puzzle to be improved
- It allows the unintended answer to be acknowledged as valid
The next obvious question is when re-asking should not be done. I believe that if the given answers fall in to either of these categories:
- Not in the spirit of the puzzle
- Requires stretching some/all of the clues (and OP confirms that correct answer fits the puzzle better)
then they are not "correct" unintended answers, and are not an indication that the puzzle is too ambiguous.
So what can we do? If a puzzle is attracting answer(s) that satisfactorily answer it, but are confirmed as unintended, we should encourage posters to re-work their puzzle. The original puzzle may be closed as Too Broad if that applies. The re-phrased puzzle should have extra/changed clues that clearly invalidate all previous answers. (If previous answers still apply, close as Duplicate). The previous puzzle's best answer, even though unintended, should be accepted, and the new puzzle should be of higher quality.
Vote up/down to indicate whether you agree!