The bigger problem for the NAACP and other race-advocacy groups is that if people can really be allowed to self-identify as whatever race they want, that would be the death knell for affirmative action.
It's already crumbling. I mean, this woman was being investigated for committing fraud on a government application by listing her race as african-american. But is there even a legal definition of what african-american is? How could she possibly be prosecuted for that? Are there any instances of schools rejecting applicants who "fraudulently" list different ethnicities? I'd be very interested to know how that has turned out.