I don't know what you are talking about. I have black friends who are very proud to be black. They never deny it. I have some mixed friends too who are proud of both of their racial backgrounds. I've never honestly seen a black person deny being black and if they mention they have white in their ancestry, they are just saying it. They don't "quickly claim" it.
I've also seen white people who say they have black in their ancestry. Likewise, they just say it and don't "quickly claim" it, as you say. What is wrong with acknowledging all of your background and all the races you come from no matter how small the percentage may be?
I understand wanting to know your background. I love my background. It's Italian, French, Irish, and German. I'm very proud of it and love the mix of cultures in my family.