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).
People seem to make a number of wrong assumptions on that, including 1) it can't also be the demonym for anyone else and 2) other countries can decide another countries demonym in their native language. Both of these things are patently false. If someone wants to use American to refer to a member of the Americas (continents) then they certainly can, but they should include enough context to disambiguate. Moreover, other nations don't decide what a nation gets to call itself in its native language. We call ourselves Americans -- so we are Americans. If other countries don't like that, well, tough for them.