In response to what your cousin said, not that isn't racist. As for the girl...
Her parents can't be too racist if they are white and adopted a chinese baby. What could be going on with this little girl is that she is noticing that she is not like everyone else in her family, and her reaction to other races could be a form of self-loathing. If she hangs out with non-whites, then people will notice that she too is not white, but if she hangs out with all whites, then maybe no one will notice that she is different. I know, twisted form of logic, but I have seen plenty of cases of this IRL.
Another factor to consider is that culture is not dictated by the color of our skin, but by our environment. If she is being raised in America, in a predominantly caucasian family, then she is culturally Caucasian-American, and may only feel comfortable with people who are culturally similar to her. Would we question her decision to have predominantly white friends if she were white?