A Mexican, Brazilian, and US citizen are all American in the same sense that a Mongolian, Chinese, and Indian are all Asian.
(edit)Also, I'm a US citizen.
It bothers me when my cousins, who have the same percentage of Italian ancestsry as I do, call themselves Italian. We were raised in moderately Italian-American households, don't speak Italian, and have never been to Italy. Personally I think it's a stretch to call ourselves Italian-American let alone fly the Italian flag.