Unless it's not his nation, United Earth is, and the UFP is just NATO.
*duh duh duhhhhhh*
The Federation is often depicted as a nation. Coffins of Starfleet officers are draped with the Federation flag, not the United Earth flag. Federation worlds don't have their own militaries, Starfleet defends all the Federation worlds. And so on.
Just imagine if the scene in Trek XI were in the modern day with a US Navy captain asking a guy in his 20s born, raised, and still living in Iowa if he's ever heard of the United States.