Bullcrap. Castro hated America, which is why I believe he chose Communism. He cooperated with the Soviets only to the point that it would help him personally, or cause problems for the US. He purged Communists from his government who tried to follow the Soviets rather than him.
Dean Rusk called it "the most dangerous crisis the world has ever seen"; Theodore Sorensen referred to it as the "Gettysburg of the Cold War." But in the end, the young President John F. Kennedy handled it brilliantly, Khrushchev backed off, and Castro went into spasms of rage. He had entered the "game of nations" as a vainglorious croupier, but the game was finally fixed by the casino owners. We know now, too, that Khrushchev was terrified at Castro's willingness to use the weapons to attack the United States directly and Castro was furious at him--this came out in later years in the famous message from Castro to Khrushchev called the "Armageddon Letter."
Blowing up the world was not the Soviets' intention, but Castro was, at any juncture where he might be cornered or destroyed, willing to resort to any measures, including most probably nuclear attacks.
(Go Israel, Go! Slap 'Em Down Hezbullies.)