Yes.. the U.S. is not NATO.. it just funds NATO more than any other member state, provides more troops to NATO than any other member state, provides arms more than any other member state, and NATO has never taken an action that works against the geopolitical interest of the U.S. But of course, they're completely separate entities. The Warsaw Pact was also famously not a mission by the SU, it was just a defensive treaty that happened to include them! A hegemon founding and funding a military alliance has no impact on that alliance, and all members of military alliances have equal rights under the treaty.

This is so much the case that until the invasion of Ukraine, France and other NATO members states were saying that Article 5 was effectively unenforceable for any member state save the U.S!