I have no idea. The more I hear the more I think the movie was referencing more real happenings than I had understood. Very early in the movie Seaman Jones (the golden ear) and rookie Beaumont are at the sonar station and Jones pulls a little training stunt. He chides the Beaumont: "like Beethoven on the computer, you have labored to produce... a biologic. ... ... A whale, Beaumont, a whale, a marine mammal that knows a hell of a lot more about sonar than you do."
I read the book. And there were certainly real references to submarine hunting. But the reference to preventing WW3 by finding a enemy sub is still lost on me.
My personal favorite of the sub movies is Phantom with Ed Harris, and it gets a little more philosophical. Basically in these kinds of dramas, escalation itself is the enemy: the move that triggers the countermove that triggers the countermove that triggers the war that ends the world
And to my knowledge, the october missile crisis has nothing to do with that movie, except submarines are the topic.