> The point is that saying someone or something is "American" shouldn't cause one to assume it's from or of the US.
That's seems like it's a pretty silly sentiment, since in common English speech that's exactly what 'American' implies.
As you yourself note, USian could just as easily refer to someone from the United States of Mexico.
I personally think it'd be salutary for our republic if my fellow Americans would refer to themselves as New Yorkers, Californians, Georgians, Texans &c. rather than as Americans (just as Germans, French, Dutch, Danish refer to themselves), but that's a different discussion altogether.