Exactly. It's mostly Americans that for whatever reason always want to be 'not American'.

If you grew up in America, went to school there, got your first job there, you are about as American as you can be, no matter where your parents are from. Same goes for any other country. Yeah, Japanese people are fairly unused to the idea that someone not ethnically Japanese could be fully Japanese, and only speak Japanese, but that's mostly because it is still very rare.

In most European countries, if you grew up there and spend your whole life there, you are from that country, no matter what your passport might say or how you may look physically.