I saw part of the Matt Lauer interview. When he quizzed her about her race, she kept using the phrase, "I identify as being black."
So, that's basically like saying, she was calling herself something...but the problem is race and color are both protected classes under Title VII of the 64 Civil Rights Act. (Sex is also listed under Title VII). This case is very much similar to when a transgendered person is hired and identifies as male or female when science and their birth certificate says otherwise.
In those cases, a lot of judges will side with employers, but being a certain sex can be an employment requirement for certain positions (server at hooters or male professional athlete, for example) Since she stepped down, they can't fire her, but she's going to have trouble finding someone to support her.
I'm not suggesting she didn't do her job and wasn't effective. I'm only stating that the color and race protected classes are what muddies the waters and are why the NAACP didn't fire her for falsifying her race on employment documents.