One might suggest that the US did exaggerate the danger in order to justify their rather elaborate and extensive reaction to the threat the missiles posed. The US military, in particular strategic command, elevated their readiness status to Defcon 2 and huge numbers of strategic forces were placed in the highest state of readiness outside of actual wartime. Most of the US fleet of B-52 bombers were dispersed and placed on 15 minute alert.
These actions may in fact not have been justified but may also have been taken in order to demonstrate to the Soviets how seriously the US were taking the threat and in order to put pressure on the Soviets to withdraw the missiles.
The Kennedy administration and others may very well have tried to exaggerate the danger in order to push others to recognize the danger of the missiles as many in the international community did not in fact believe that the Russians were placing medium range missiles in Cuba.
Especially given that the United States already felt that a similar capability was available to them thanks to the deployment of Polaris missiles on board ballistic missile submarines, their posturing may have been exaggerated in order to suggest that their removal of the missiles in Turkey really was a major concession when in fact it was not.