Well, a lot of people have already said it, but...
1) North America is the U.S., Canada, Mexico, Greenland, and all Central American countries. Half of Iceland is also on the North American continental shelf.
2) I'm sorry, but I think that getting all worked up over referring colloquially to the U.S. as "America" is ridiculous. Frankly, if you're looking for trouble, referring to the U.S. as "The States," as Canada often does, can be equally interpreted as a slight against Mexico, as it is officially called the "United Mexican States." Considering the names of the countries, it is easiest to call them Canadians, Mexicans, and Americans. And all three are part of the North American continent.