CONTEXT— Am I wrong for referring to The United States as ‘America’?

My friend from Quebec showed me photos of his night sky, and I jokingly said, “Alright, we get it, Canada is better than America.” He replied, “Canada is in America.” He wasn’t claiming Canada is part of the USA. He was correcting me on the basis that Canada is in North America. I understand that point, and technically he’s correct. However, as an American, I was using “America” as shorthand for the United States, which is a very common usage. Since I clearly meant the USA and not North America, it feels like he misunderstood my intent and corrected me based on a technicality. Was that a fair correction, or was it unnecessarily pedantic?