after all, a Brazilian is an American, seeing as they live in South America.

A citizen of the United States of America is rather more specific.

Part of the problem I see with political discourse in North America is the concentration on persons, with not enough talk about citizenship. See, persons have rights, citizens have responsibilities. This works really well for large corporations, as they are persons in the law, and gets people talking about their rights instead of their responsibilities. OTOH, if the discourse is concentrated on citizenship, then the corporations don't really have much to say since they aren't and cannot be citizens.

Now, if I hop across the border to visit Watertown, New York, I'm in the country legally. Does that make me an "American"? It sure doesn't make me a citizen of the US. It also doesn't make me part of the culture that surrounds citizenship in the US.

We gotta spend more time talking about citizenship in our political discourse, because the corporations can't enter that conversation, which means that it's a conversation that happens among human beings, not institutions... after all, the government of Canada is a duly incorporated entity, not a citizen.