Depends where you're talking about. Around here, the only hint that you're not dealing with Europeans is that we smile more and take more showers.
Trying to identify that quintessential thing that makes people American is virtually impossible, especially since people don't give up their cultural beliefs when they immigrate. Choose the right part of the US and you'd never know you were in the US, if not for the signs.
Trust me, not counting recent Irish immigrants, I could recognize a American even without the accent.
Accent's a different matter.
No American is going to miss that as English language accents are something that we pay very close attention to. But, given that most English speakers in the world have some sort of an American accent, it seems a bit odd, to expect anything else.
You're statistically most likely to run into an American English speaker if it's truly random.
Anyways, I don't really care, I just think that folks are stretching a bit to draw a conclusion that doesn't really follow.