Inside Argentina, if someone ask me where I'm from I', expected to specify the province where I'm from. (And in some cases, the part of the province, like "Santa Fe" and "Rosario".) My guess is that it happens in all countries. But if I talk with people that lives abroad, usually "Argentina" is enough. The US is not special in this.
Whether you like it or not, it's usually insufficient for someone from the US to simply say that they're from the US. It's a big enough place with enough externally-visible cultural variation that people want to know.