I would say that this statement is not true in any serious way.
For the statement to be true, we would have to assume that neither the US nor the Soviet Union would have used nuclear weapons in this crisis. While we may hope that they would not have, there is no evidence that that is the case.
When the Soviet missiles were discovered in Cuba, President Kennedy and his advisers all agreed that they had to be removed no matter what. They considered air strikes against Cuba and they considered invading the island. It seems likely that either of these actions could have triggered a nuclear war. Similarly, it seems likely that a Soviet attempt to run the blockade could have led to war. If the US was (as it appears to have been) determined to blockade Cuba, it would have had to attack any Soviet ship trying to break the blockade. This would have been an act of war.
There are many ways that the Cuban Missile Crisis could have led to an actual war. In such a war, it is likely that nuclear weapons would have been used. Therefore, the Cuban Missile Crisis was a real danger to the world.
To a large extent it all depends on the perspective of the discussion. If it is simply focused on the tactical nature of the weapons and the effects of their possible use, it would be relatively difficult to overstate the danger of those weapons being in such close proximity to the United States, particularly the East Coast. The only nuclear weapon that could arguably be deployed that would give as little warning time as surface to surface missiles fired from Cuba would be missiles launched from submarines off the Eastern seaboard which the Soviets had great difficulty deploying as US technology was so far ahead in the underwater arena.
So the one way that one could argue that the danger was overstated is that simply no one actually wanted to start a nuclear confrontation given the principal of mutually assured destruction or MAD. The idea that the Soviet's first strike capability received a massive upgrade from the missiles is important, but Kruschev (hopefully) could not have seriously considered using them
The second part of the exaggeration usually comes with the emphasis on the stand off at sea and the blockade. It is important to note that while those were going on the back-channel negotiations were in full swing so the public face of the crisis appeared significantly more serious than it did to those who were "in the know."