Having only read that second post, what said poster pointed out is indeed correct since North America is not a country. Regardless...
Going to go with what Anouleth, Reojew, Esau of Isaac, and Balcerzak said and also add the USSR as another example of how we take the name of a (former) country and shorten it to something like the soviet union for simplicities sake.
Also: http://www.thefreedictionary.com/America
http://en.wikipedia.org/wiki/Americas "In the English language, the Americas refers to the landmasses of North America and South America with their associated islands and regions, whereas America, in current usage, usually refers to the United States of America."
Additionally, the USA seems to be the only country in the world that uses the word "America" in its countries name anyway.
I think if I meet someone in real life who said that you can't refer to the USA as America I would just laugh at them and tell them to look up what the word means in a dictionary or something like that. I mean really, of all the things that you're getting pissed off about you're going to pick something like this?