Late to this conversation, just a couple of things to add.
I see no reason to keep a misidentification issue private since the relevant image is public. To each their own of course, this is just my point of view. The public stands to benefit from witnessing the discussion, even if they don't join in. If it's an obvious entry error (like two images in sequence whose tags are switched) then I would make the contact privately in order to reduce noise on the forums.
What is interesting to me is that people have sometimes taken my requests that images be moved in quite the opposite way of how they were intended, like as some personal affront instead of a gentle suggestion open to feedback. While I always have something I can refine about my language or approach, I do not see any other positive outcome from this kind of response. Especially when an admin has to become involved to resolve it. It arises from a fundamental misunderstanding about the way the site functions -- to quote the line above which is most apt, we all need each other.
As I have seen in excess with certain plants (tagged by nurseries under the wrong name, and always the same wrong name) it can be quite helpful that the ID questions remain public because then the other users of the site are alerted about the potential issue. And I do think it's important to ask for feedback rather than simply asserting contrary truth, it just levels out the playing field and invites continued participation. And rather than titling the thread "Wrong ID" I would prefer to title it "ID question". Those are considerations of tact, really. Fully realized by the participants in this thread, of course.