I would favor leaving the question itself alone and explaining the difference in the answer.
This situation reminds me of questions on Stack Overflow or Computer Science which are founded on misunderstandings or incorrect principles due to the questioner's inexperience with the subject. On those sites it's pretty common to downvote and close such questions, which I don't agree with, so we're already one step ahead: whether we edit or explain in answers, we're still teaching the questioner something they hadn't known before.
The reason I favor explaining in answers is that an answer is a much better venue for teaching the questioner something than an edit is. verbose's explanation in the linked answer is brilliant, and it engages with the questioner at their current level of understanding, whereas the best we could do in an edit is change the language to match the question as it would be written by someone who already understands this distinction. This could well leave the questioner looking at the edited version and wondering what exactly was wrong with what they originally wrote. Instead of directly teaching them something, it forces them into a game of "Spot ten differences between this edited post and your original post".
Of course, if we get lots of questions like this, it'll get tedious explaining this all the time. And we will probably get lots of questions like this; I've already seen plenty of posts on Meta talking about how the author's word and intent should be the gold standard for evidence in answers, which just isn't how most literary analysis works. So the best solution might be to write a canonical question, something like "What is the intentional fallacy?", that explains the distinction. If we see a question that commits this fallacy, we can mention that the question isn't specific enough to answer as is and point them at this canonical question as a guide for making edits. If it becomes a big enough problem we can start closing as "unclear what you're asking" until the edits are made.
The benefit I see for having a canonical question is that we avoid repeating the same explanation in dozens or hundreds of answers, but we still have the flexibility that an answer offers for teaching a concept instead of having to monkey-see monkey-do it with edits.
In the best case, the questioner understands what needs to be done to fix their question and does it on their own without further interference. But if a questioner still doesn't understand what needs to be done, or doesn't feel capable of doing it, then we can still make edits ourselves to bring the question on-topic, while also addressing the questioner's specific confusions.
In effect, this process can serve as a sort of workshop on the intentional fallacy for those questioners who are willing to learn: they get a general explanation of the concept from the canonical question, but they can also get help on their specific case from comments or edits made by helpful community members. This way, even if someone other than the questioner has to make the edits, the questioner at least has a reference point for the purpose of the edits was. This might also be a useful model to adopt for other issues where questioners' instincts are at odds with accepted practice in literary criticism.