U.S. citizen and U.S. national are not the same thing. There are some, but very few, U.S. nationals who are not U.S. citizens (currently mainly people born on American Samoa and their descendents, and some others). U.S. nationals, whether citizens or not, can get U.S. passports. And on the U.S. passport application you sign a statement saying you are a U.S. citizen or non-citizen national. So technically, signing that statement is not necessarily a claim of U.S. citizenship.