http://www.jfklibrary.org/JFK/JFK-in-History/Cuban-Missile-C...

> No one was sure how Soviet leader Nikita Khrushchev would respond to the naval blockade and U.S. demands. But the leaders of both superpowers recognized the devastating possibility of a nuclear war and publicly agreed to a deal in which the Soviets would dismantle the weapon sites in exchange for a pledge from the United States not to invade Cuba. In a separate deal, which remained secret for more than twenty-five years, the United States also agreed to remove its nuclear missiles from Turkey. Although the Soviets removed their missiles from Cuba, they escalated the building of their military arsenal; the missile crisis was over, the arms race was not.

http://www.history.com/topics/cold-war/cuban-missile-crisis

> During the Cuban Missile Crisis, leaders of the U.S. and the Soviet Union engaged in a tense, 13-day political and military standoff in October 1962 over the installation of nuclear-armed Soviet missiles on Cuba, just 90 miles from U.S. shores. In a TV address on October 22, 1962, President John Kennedy (1917-63) notified Americans about the presence of the missiles, explained his decision to enact a naval blockade around Cuba and made it clear the U.S. was prepared to use military force if necessary to neutralize this perceived threat to national security. Following this news, many people feared the world was on the brink of nuclear war. However, disaster was avoided when the U.S. agreed to Soviet leader Nikita Khrushchev’s (1894-1971) offer to remove the Cuban missiles in exchange for the U.S. promising not to invade Cuba. Kennedy also secretly agreed to remove U.S. missiles from Turkey.

http://www.theatlantic.com/magazine/archive/2013/01/the-real...

> Once that was straightened out, Kennedy himself declared repeatedly that the Jupiter missiles were “the same” as the Soviet missiles in Cuba. Rusk, in discussing the Soviet motivation for sending missiles to Cuba, cited CIA Director John McCone’s view that Khrushchev “knows that we have a substantial nuclear superiority … He also knows that we don’t really live under fear of his nuclear weapons to the extent that he has to live under fear of ours. Also, we have nuclear weapons nearby, in Turkey.” The chairman of the Joint Chiefs of Staff, Maxwell Taylor, had already acknowledged that the Soviets’ primary purpose in installing missiles in Cuba was “to supplement their rather defective ICBM system.”

> if the administration’s domestic political priorities alone dictated the removal of the Cuban missiles, a solution to Kennedy’s problem would have seemed pretty obvious: instead of a public ultimatum demanding that the Soviets withdraw their missiles from Cuba, a private agreement between the superpowers to remove both Moscow’s missiles in Cuba and Washington’s missiles in Turkey. (Recall that the Kennedy administration discovered the missiles on October 16, but only announced its discovery to the American public and the Soviets and issued its ultimatum on the 22nd.)

These are all US-based sources so I'm not sure what gave you that impression unless you only heard about it in the 60s/70s when it was embargoed/classified?