My co-worker friend is from Mexico. He is American. I don't mean "Mexican American" like the Cheech and Chong song; "Im a Mexican American, I take Spanish at the junior college, and get a B".
He pointed out to me that when people talk about American, they're refering to the US. "American Idol", "America's Got Talent", "America the Beautiful", "God Bless America" and on and on. But here it's actually the United States of America, part of North America along with Canada and Mexico. Then there's Central America and South America. Now you're probably thinking "duh, shitforbrains, I've known that since elementary school". But pay attention to how often "America" is used in place of "United States of America".
My buddy believes that it's another way for the US to posess more power around the world by using tricky language. Like "freedom fighters". George Carlin said "fire fighters fight fire, crime fighters fight crime, what exactly are the freedom fighters fighting?"