I agree somewhat, but Square's supervisory role doesn't necessarily imply direct involvement. As I understand it, Sakaguchi and Uematsu had veto power over the operation, which they obviously chose not to exercise. I suppose that could be taken as mute testimony to the legitimacy of LotC, but I think you would agree with me when I say that it doesn't fall into the same category of sequels as X-2 or any of the Compilation projects.

Given that Square was not really the primary agent in the creation and distribution of LotC, I suppose I would compare it to the plethora of Star Wars novels that take up the story after Return of the Jedi. There's a kind of legitimacy, to be sure, but they wouldn't qualify as sequels in the same way as, say, an Episode VII would.