If a post contains inaccurate information it would not be ideal to mark it "Unhelpful". Instead, you should reply to the thread by posting the correct information. If there were a Helpful button your more accurate reply should attract clicks.
If I do receive an Alert indicating that a post is inaccurate (rather than misplaced or disruptive) I either post a reply as described in the previous paragraph, or contact the poster and suggest an edit, but anyone could contact any poster by PM (unless the member has opted out of the feature) to suggest an edit.
But we're not talking about a moderator editing a post here, we're talking (or at least the way I read it) about a post marked as helpful when it is not in fact that and what action a moderator is/is not to take-and THAT is a very big difference as I personally don't think moderators should be acting on what other members like/dislike/find helpful as then moderators are changing the opinion of another member. And with all of that, no one who has proposed or is actively supporting this issue has stated how that comes into play (or answered other questions for that matter but I digress)