Well I'm Chinese Canadian, and I look like some famous guy from Hong Kong. Lots of people have said the same thing, and I never thought there was a need to be offended. I look Chinese, and that's because my parents are from Hong Kong. Well actually, I apparently look Korean. Some people say Japanese, but whatever. It's what people see. Being born in Canada doesn't change the fact that I look like a group of people half-way across the world.
It's not exactly what I'd consider racist, but I guess some people have a different definition of the term.
Don't take this the wrong way but I thought you were Japanese... I used to think I could tell the various Asian countries apart by looks. I had Japanese-American neighbours. The daughter was purty cute too.