I think a game could straddle the US/Canadian or US/Mexican border. I also think China would work well since communism played such a large role in 50s Americana. A game set in China would probably require that the US had established a large enough beachhead there before the war that remnants had survived. Other communist regions like Russia and Eastern Europe might work but I think it would be stretching things without an actual American presence.
"America" is the colloquial name for the country, and you knew exactly what people were talking about so why make a fuss about technicalities? It's the same as saying that Britain isn't a country since it's actually the United Kingdom, or rather it's actually the United Kingdom of Great Britain and Northern Ireland. Unless you can maintain your high standards yourself by always using the technically correct national terms I suggest you not criticize others.
However this is off topic, if you really must discuss this issue then start a thread in Community Discussion, don't continue it here. I will note that if you do make a thread ensure it lacks any hint of being confrontational or critical or it will likely devolve in to a mess of nation-bashing and get locked.