I mean Neil Armstrong literally smoked and did not "believe" in excercise so they were absolutely not the most physically fittest people. They were just freaks in terms of enduring a lot of stress tests. Physical endurance is just one aspect they train for. Other aspects were much more valued like them being military flight pilots/smart enough to understand the systems/mentally strong enough to not break down etc. You were not selecting for absolute raw fitness for the apollo missions.
They didn't select for pure physical fitness but they were already selected for fitness as a pilot and then again when they were selected from the pilots to train as an astonaut. Its not like they just picked arbitrarily from the potential pool of candidates and gambled on getting better than average.
Again, they don't select for pure fitness when it comes to pilots as well. The fact is that you didn't need to be super fit to handle those crafts. Fitness today is much more prioritized because astronauts spend exponentially longer time in space now than they did then and they have to work out in space to keep their bodies from getting used to being in space and zero gravity. They now spends months in space, previously max they would go for is like a week.
So no, pilots or astronauts are not "some of the most physically fittest people in America". They were exceptional human beings but lets be realistic.
Armstrong literally did not believe in physical excercise though. He thought the human heart had a fixed number of beats and didn't want to "waste" them. Look it up. They guys really did not care about physical fitness back then.
Whether he believed in it or not, he passed rigorous physical tests for the Navy and NASA. They don't let just any slob be a fighter pilot, much less a test pilot or astronaut. If you don't have good cardiovascular fitness, you can't handle high G-forces or maintain good judgement while sleep deprived (those jets didn't fly themselves while the pilot napped like modern ones do).
Maybe he was just naturally fit. Some people are. But he was undoubtedly fit.
Look up those tests and see what they selected for, its not as much as raw physical fitness but rather how their bodies reacted to stress + a host of other pyschological factors + flight training. Yes, it is without a fact that they are no slobs but calling them the most fittest is also hyperbole and paints this image of hyper fit astronauts which wasn't true back then. They also didn't care much about long term effects of space travel on the body back then because missions were very short back then.