Choose Your Race?

In my sociology class, we were talking about Rachel Dolezal. If any of you aren't familiar with her, she's a white woman who was born to a white family but identifies as black. She managed to get herself a spot in the NAACP and teaches a Black History course at a predominately black university. It only recently came out that neither of her parents are African American in decent, but had adopted African American children who Rachel grew up with. She claims that because of her connection to her siblings, she feels more black than white. She's gotten a lot of backlash for this now that the truth has come out. (I honestly don't remember what she did to change her skin and hair, but I know she did it herself) So my question is, do you think people can identify as a different race than they're born with? Just because they have a "connection" to it but it's not in their biology?