Yeah, that was after the blockade began, which was Kennedy’s idea. Against the advice of the military.Nuclear war was not stopped by Kennedy - a Russian sub officer, who didn't know whether WWIII had started or not, convinced his fellow officers not to launch his nuclear torpedoes when US Destroyers were dropping depth charges on them.
On Oct. 27, 1962, the world was close to a full-scale confrontation between the two nuclear superpowers. As the U.S. Navy pursued Soviet submarines armed with nuclear torpedoes off the coast of Cuba, only the composure of Captain Vasily Arkhipov saved the world.www.rbth.com
As the story states, the crisis was over the next day - after Kennedy agreed to withdraw missiles from Turkey.
Now, imagine a scenario in which the US invades or sends air strikes that DOESN’T result in nuclear war. It’s very hard to do that.
Also, the missiles withdrawn from Turkey were already obsolete by that point. Besides, the soviets kind of had a point. Why should they allow missiles in their back yard if the US wouldn’t allow them in theirs?