I doubt it. Sounds like another one of these myths put forth to make JFK seem like a larger than life god. I really doubt a bomber could penetrate that far into Russian airspace.
The Cuban missile crisis ended when JFK surrendered to the Soviets by giving in to their demands to remove US missile bases from Turkey. This is what the Soviets wanted all along. But the Soviets agreed to take their missiles out of Cuba in exchange for an ex post facto announcement that the US was pulling its nukes out of Turkey. Khruschev simply allowed JFK to wait a little while before making the announcement to save face and so it wouldn't appear we were bowing to Soviet pressure. Make no mistake about it, despite the historical revisionism about how JFK the superhero faced down the Soviets, the Soviets really in the end won this one.
The top speed of the suckers was mach 2.1 though.