The mistake you're making is taking a politican's words at face value. If you were to ask JFK he'd say militarily the US couldn't accept nuclear missiles in Cuba. But our own military was willing to accept it, in fact that was one of the options presented to him: do nothing. The reason he did something was all political, because he was running for reelection, needed to look strong on the topic after the Bay of Pigs, and had publicly committed to not accepting missiles in Cuba earlier (as the Soviets had also publicly asserted they wouldn't put them in Cuba).

The book "Essence of Decision: Explaining the Cuban Missile Crisis" is somewhat regarded as a classic here that is worth reading.

Also, worth pointing out that I too can quote a Khrushchev (Nikita):

Q. How much did the crisis have to do with U.S. Jupiter missiles deployed in Turkey?

A. Zero. The missiles in Turkey were the same as the missiles in Italy and Great Britain. Why do you make the difference between those three missile bases? They are the same. They are the just the first step in a standoff confrontation in 1962 when both sides began to deploy missiles in their own territories. Those missiles in Turkey would be removed from Turkey anyway in two or three years.

From what I've read, most historians would agree with that take.