I'm 100% american, sound american, look american (northeast/slightly boston accent).
Today was my first day with new students. I asked the first class if I was British (after talking for a good 5-10 minutes.) Most answered yes. Then, the second class I said "where am I from?" and a few shyly answered "Australia?" I laughed and said no, then almost in unison they cried out "ENGLAND!"
These are college sophomores! But apparently tricking them would not be too hard.
And it's true that american identify ourselves by our state, but I have given that up in china long ago because of the confusion it brings. The only people I see stick to their state long-term in China are New Yorkers. They can't have people think they're from somewhere less than there. hahaha