It should go without saying, but "the free" in "the land of the free" refers to Americans, not everyone else. Not sure if you were trying to make it sound like a great irony that "the land of the free" would exclude or ban people, but if so it doesn't quite hit the mark. A more cutting criticism would be that the land of the free isn't letting one of its own companies freely compete.
Also worth pointing out that most Americans don't have passports and getting one can take anywhere from 6 weeks to 6 months.
Also, you'd have to be smoking something to assume that the three letter agencies are not going to be combing through Anthropic's customer list and assessing for fraud and foreign bad-actors. If you lie, they'll probably catch you eventually and most people are not stupid enough to lie about their identity to the US government and think they'll get away with it forever.