X men First Class and the Cuban missile crisis

I don't know much about the Cuban missile crisis and after I saw the latest Xmen movie it got me curious. Did the Russian’s really blow up one of their ships to prevent a war or was that something the filmmakers change to add suspense to the story?

I can't find a reference to a Soviet ship being destroyed by one of it's own as the catalyst for ending the crisis. From what I recall of the movie 13 Days, there was a lot of on-the-edge politics, negotiations, and intelligence gathering operations. Military skirmishes complicated the negotiations, but it seems like in the end negotiations won the day and defused the crisis. Combat losses were the price of keeping the peace by way of each side rattling their sabers at each other, but not a deal breaker; it looks like secret negotiations calmed things down (something about the U.S. withdrawing missles from Italy and Turkey, and the U.S.S.R. would withdraw the missles in Cuba).