I'd argue that being morally correct *is* being factually correct, though I don't know the context of her statement. We have to respect truth if we want to be moral. Morality is about doing good in the world, not masturbatory celebration of the awesomeness of your self.
I think that's a grossly immoral attitude, but more than that, I don't think if pressed, you'd actually act as if that were true. "Oh well, people in that neighborhood killed my mom. To me, that's immoral, but I respect that it's just their custom."
My thinking is that subjectively, no one behaves as if they truly believe that morality is subjective. Objectively, it is hard to find a basis, but that's probably related to it being a difficult issue rather than to it being an impossible one. The fact that people inevitably make mistakes doesn't mean that truth doesn't exist.