It also ignores most colloquial usage of the terms America and American in English. While technically correct, it is unlikely to occur. Americans are citizens of the United States of America. Just as Mexicans are citizens of Estados Unidos Mexicanos. But we shorten them to Mexicans as well.
Its more useful in either case to just list your nationality in either case. Unless people seem to want to identify with an Italian name for both continents I don't see where getting all up in arms over Americans referring to a citizen of the US. USian is an alternative, but lets be honest, it rolls off the tongue horridly and is unlikely to catch on.
Also, it's an unsolvable problem, because there is no part of "United States of America" that is technically unique. It's not the only nation on the American continents, and it's not the only nation whose official name includes "United States" (Mexico does as well).