She can, but the rub comes when she only starts telling everyone she identifies as black when it comes out she lied about it in the past.
Same thing would have happened to Bruce Jenner if he tried to enter the Olympics as a woman and got caught, then tries to say its because he identifies being a woman.
All of it is a bit much... whats next? Saying I'm a MIT ngineering graduate when it turns out I only "identify" as being a graduate?