That is not the issue.
Khruschev saying stuff did not make it true, and JFK as president had the intelligence data to know how many missiles the Soviets had. The Soviets had been invaded by the Nazis and millions of them were killed. The US had previously invaded the USSR after the Revolution. No one invaded the US in WII unless you count a couple of useless Aleutian islands. The Soviets had certainly never invaded the USA..
Khruschev had replaced Stalin, he was a Ukranian in a mostly Russian federation, and he was trying to prove that he was up to the job. Many Ukrainians collaborated with the Nazis during WWII and the Russians did not entirely trust his leadership.
The issue is that the US had vastly more missiles than the Russians, and at least one base in Turkey, not 90 miles from the border, but right on the border of the USSR before the Soviets set up bases in Cuba. None of this was mentioned in the press in the US. JFK and following presidents p!ssed away fortunes on missiles that were never used. The Soviets did the same. It was a huge waste of resources. The Cold War was stupid, just like telling me and my classmates that the USSR was likely to bomb Kansas City next Thursday and we could save ourselves by hunching under our desks.