There is a shit ton who do not. I went to school with a lot of Puerto Ricans who you wouldn't know they weren't regular white until they opened their mouth and spoke Spanish. They did not at all identify as black.
I don't think they were claiming White. More like Puerto Rican was their identity without a racial layer.
********** "Everyone has a plan until you punch them in the face. Then they don't have a plan anymore." (c) Mike Tyson