Not mentioned in the ADN article was that another Alaskan island, Kiska, was also invaded and occupied.  However, when the joint American-Canadian force landed on Kiska, they found that the Japanese had left.  There were casualties on Kiska because of friendly fire incidents.  The Canadians were from units posted in Canada only for "domestic" assignments, but domestic was expanded to be western hemisphere.  The Canadian role is rarely mentioned, and the photographs all show soldiers in American uniforms, which is what the Canadians wore on this invasion.
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Thus, because of this Canadian force, the last time the US was invaded by foreign soldiers was not in the War of 1812 by British soldiers, but rather in WWII by Canadian soldiers on Kiska.  Yes, they were friendly soldiers, and invading by invitation, but they were still foreign soldiers.  See if you can win some bets with that one.