Race is arbitrary and silly. I am white skinned with blue eyes and blonde hair, yet I have Angolan, Madagascar, Khoisan, Indian (Bengal and Tamil), Indonesian and Chinese heritage from about 350 years ago when my ancestors left Europe for South Africa and took wives from amongst their slaves as well as freedwomen and their daughters. Obviously this was diluted by centuries of Europeans thereafter, but those people are as much my ancestors as any other.
We in South Africa then implemented Apartheid (Segregation in Afrikaans) and have been struggling with the consequences ever since, while none of us did not have some colouring in us.
External racial classifications are more trouble than they are worth. In my opinion, racial classifications should be abolished as well as affirmative action. It is insulting to minorities to give them a hand up as if they are inferior to the majority and need things to be easier for them. This then perpetuates ideas of inferiority as the majority students will automatically assume that the minorities are dumber etc. than they are and this attitude will carry over into their careers and hiring practices.
Everyone should be placed on an even playing field. No advantage merely due to an accident of genetics should be tolerated, even if historically they were underprivileged. They could rather invest more in minority schooling etc. than impose quotas and lowering entrance standards and such. But even such programs cannot be allowed to continue forever or you are merely institutionalising a reverse form of discrimination.
Besides, you never know what weird branch is hiding in your genealogical tree (For instance many black Moors came over into Spain in the Middle-Ages and served under Frederick II in Italy and Germany. It is likely that many Spanish, Italian and German families have black ancestry from 800 years ago that they are unaware of).
Let the girl call herself whatever she wants. It shouldn't matter. The fact that it does is an indictment of society in general.