Idont believe that JFK saved the world, while I do think he always tried to do the right thing, in this case he brought the world very close to nuclear war. The soviets supposedly backed down, but very few people seem to know that part of the deal with USSR is that the
US remove its missiles from TURkey, (what were they doing there?)

During the crisis, the US set up a naval blockade, and what was one of the first things they encountered? A Soviet sub. They fired a depth charge (a distance away from it) as a signal to surface. Although they were unaware that the Soviet sub had lost radio contact
with the USSR and that the Captain had the ability to launch nuclear
weapons - at his discretion (this fact only came out in the 90s after the collapse of the USSR, to which MacNamara (defense sec. at the time) that was the closest the world came to nuclear war.

the missiles in cuba and Turkey were irrelevant within a few years,
when the large nuclear subs of both nations carried enough warheads to destroy all the major cities of the either country.