I think some countries have a definite "look." Not so much that you can't be that nationality if you don't have the look, but that if you have the look you are probably of that nationality. I've had a Russian roommate and several friends, and they all have a certain look to the cheekbones that is distinctive. I'm sure there are plenty of Russians who *don't* have that look, and many Americans of Russian descent that do (my friends had lived here since childhood but were born in Russia), but it hints in that direction.
That said, America in particular is such a melting pot, that I can't really imagine any possible look that couldn't be American. While I will often guess, when I see somebody who has very Nigerian features, that they are a recent immigrant, it's not because they *couldn't* be American, but just that the area I lived in had a lot of Nigerian immigrants (rather than Americans of Nigerian descent). Purely based on immigration trends in the locale.
I could see somebody not looking native to a country that had a low rate of immigration, or a country that's immigration was so recent that there weren't weren't any different-looking natives, but... America, of all countries?