It is accepted practice that "America" refers to the USA and not all of North America or South America. For example, you would call a citizen of the USA an "American", not a "USA'ian" or "United States of American". No disrespect to the other countries in North/South America is meant or implied 
http://en.wikipedia.org/wiki/United_States
"The United States of America (also called the United States, the U.S., the USA, America, and the States)..."
If by "accepted" you mean
you accept it, then yes, it is accepted. I'm sure you know many people in that train of though. My experience is different, though.
Maxtog, I consider you a respectable forum member. IMO, your posts contribute and you seem to know how to keep your voice down and make it count when you raise it. But regarding the name of the country, essentially only the lack of a better gentilic (in the English language, anyway) is what somehow justifies the arrogation of the word "American" to denote people from the US, but "America" is still a continent made up of 35 countries (recognized by the UN, at least). Again, if you haven't, let me suggest you to research into the origins of the name of USA. It's a very interesting read.
Now, regarding the gentilic, one could liken the situation with
Estados Unidos Mexicanos, or
Estados Unidos do Brasil until 1968, or some others, but they have the advantage of being
United States of something that doesn't denote anything else that precedes them (in this case, by almost 3 centuries). We could drift into an otherwise interesting discussion about the 5 or 7 continents model or such not unimportant technicalities, but the fact remains: somebody from Chile is American, as is somebody from Canada or Ecuador. Just like a Croatian or a Swede are Europeans. I'm not a native English speaker so if in this language you call yourself "martians" I'll play along. Come to think of it, picturesque characters like Fidel Castro and Hugo Chavez refer to people from the US as "americanos".
And thanks for the link. Wikipedia is always on the top of my list for reliable sources of information.
[Oh, oh... smells to Jim sharpening his axe... or was it a sword...]
