But what about all the old fat people in the TOS movies, they couldn't do sit ups.
Ah, but that's what they have age brackets for. At Kirk's age, he probably had to manage like...ten or so sit-ups to pass. Also, he probably would have had what they call a "profile" in the Army today - he's too old and broke, so the doctor would excuse him from certain events. Like, for instance, in my experience, I have met very few people over the age of 40 or so in the Army that still have to run for their test (they do a 2.5 mile speed walk instead.) This is because all those years of running has pretty much made their knees completely shot. And poor Harry, being a young whippersnapper in his 20s during the show would have been in the most difficult age bracket to pass the test.