S. and had been at least since the launching of Sputnik, an event which showed the West that it had to hurry in order to prevent the Soviets from taking over space and raining missiles down on their enemies. The Cuban Missile Crisis was a case in which the President of the United States took a direct stand against an action by the Soviets, the action of sending missiles to Cuba. President Kennedy invoked the Monroe Doctrine and told the Soviets to keep their hands off the nations of this hemisphere, and ultimately the Soviets did back down. Ever since that time, there have been arguments as to precisely what happened, how these events occurred, and how close the world came to nuclear war. The filmmakers would not have known about the missile crisis when they made this film, though fortuitously the crisis occurred once the film was in release and so may have caused many people to go see it.
The background to the story includes references to the Korean War, the conflict in which the soldiers were engaged when they were captured and brainwashed. American involvement in that conflict would have been readily understood by the audience of the time, a conflict in which American troops had been sent to assist the South, a conflict that was not fully resolved then and remains a concern to this day. Tensions in the world were apparent in more places than just Korea, and the United States at the time was encountering increased challenges from other quarters.