"Correct" is closely connected with a moral "ought", which in turn has a number of different definitions (and thus connotations) depending on who you speak with. The statement "it would be correct for Clippy to exterminate humanity and turn the planet into a paperclip factory" might be technically right if we equate "stable" and "correct", but it sure does sound odd. People who are already into the jargon might be fine with it, but it's certain to create unneeded misunderstandings with newcomers.

Also, I suspect that taking a criteria like stability under reflection and calling it correctness may act as a semantic stopsign. If we just call it stability, it's easier to ask questions like "should we require moral judgements to be stable" and "are there things other than stability that we should require". If we call it correctness, we have already framed the default hypothesis as "stability is the thing that's required".