NEW YORK (CBSNewYork/CBS News) — The president of the Spokane, Washington chapter of the NAACP is being accused of falsely portraying herself as a black woman, but an NYU professor said some people can, in fact, identify with a race other than their own.

As CBS2’s Weijia Jiang reported Friday night, Rachel Dolezal was asked in an interview if she was African-American, and was clearly taken aback as she answered, with the remark, “I don’t understand the question.”

In a different interview, with Spokane CBS affiliate KREM-TV, she said: “Actually, I don’t like the term African-American; I prefer black. So, if asked, I would say, yes, I consider myself to be black.”

But her biological parents say that is not true. Her birth certificate lists her parents as Ruthanne and Larry Dolezal, who said their daughter has been estranged from their family and has been misrepresenting herself.

“Our daughter is primarily German and Czech and of European descent,” Ruthanne Dolezal said. “She’s white.”

The couple said their daughter is pretending to be someone she’s not, CBS News reported.

“Rachel has wanted to be somebody she’s not. She’s chosen not to just be herself but to represent herself as an African-American woman or a biracial person,” Ruthanne said.

But NYU sociology professor Ann Morning told CBS2’s Jiang that just like some people are transgender, others may be trans-racial – identifying more with a race other than their own.

Dolezal grew up with four adopted black siblings, and was briefly married to a black man.

“We’re getting more and more used to the idea that people’s racial affiliation and identity and sense of belonging can change, or can vary, with different circumstances,” Morning said.

Dolezal’s biography at Eastern Washington University says she received her master’s degree from Howard University, a historically black college in Washington, D.C., CBS News reported.

KREM-TV obtained police reports in which Dolezal claims to be the victim of several hate crimes. They found that police responded but no suspects were identified and no arrests were ever made, CBS News reported.

Dolezal said the only ones questioning her identity are Larry and Ruthanne.

“I don’t give two (expletive) what they think,” Dolezal said.

“It’s more important for me to clarify that with the black community and my executive board than with people who don’t understand,” she said.

In the past, Dolezal has identified herself as a mix of black, white and Native American. She dismisses the controversy as little more than an ugly byproduct of family dysfunction, CBS News reported.

Many Dolezal critics have no problem with her race – whatever it may be – or her physical appearance. Instead, they are troubled by her motives.

“For someone who’s a black advocate, you know, to go and get yourself elected to a board to advocate for black people, but deny black people the self-determination to decide who they want to elect is a problem,” Morehouse College professor Marc Lamont Hill said on CNN Friday. “Plenty of white folk have led NAACPs, but we knew they were white.”

In a statement, the NAACP said, “One’s racial identity is not a qualifying criteria or disqualifying standard for NAACP leadership.” The organization said it stands behind her.