I think it really comes down how culturally connected you feel you are to China. If your parents are chinese but raised you really western you might not feel as chinese as someone who's parents kept a lot of their own culture or integrated chinese culture in with american or british or w/e you are's culture
If you think about, being Chinese is a fact. If someone believes that there nationalism is in some other country like Britain, in that sense they can say that there British. That's why Chinese people born in America are considered to be Chinese Americans.
I was born in vietnam...to chinese parents...still I go around telling people I meet that I'm full chinese. There!
I consider myself Canadian. It's hard to consider yourself Chinese when you have never step foot in a country, don't understand the culture and hardly speak the language.