Personally I'd label "the Cuban Missile Crisis" a "failed US invasion of Cuba". Within that context, it fits into the many failed US invasions of Cuba (from Teddy Roosevelt to the Guantanamo Bay...I'll let the reader supply their own words for that.)

Within the context of my historical expertise, I would point out that the USSR and USA were engaged in ongoing struggles regarding "air superiority" and "space superiority". UFO reports fit into this because "UFOs" routinely violated USA airspace. At various times, various people in the USA considered some "UFOs" to be Soviet in origin. In the famous summer of '47 with the American "flying saucer" flap, a Gallup Poll indicated that Americans considered "Soviet" to be one of the most likely explanations for the odd reports. I'm not personally familiar with similar polls about "UFOs" during directly around the Cuban Missile Crisis, but presumably some Americans considered the Soviet Hypothesis as well as the ET Hypothesis.

People who were central to the Kennedy Administration's decisions about "the Cuban Missile Crisis" had varying exposure to these concepts. Kissinger of course thought he knew everything (a shallow understanding of game theory can spoil a person's decision making process), and was very interested in "controlling outer space" as a dimension to project nuclear domination. Curtis LeMay apparently advocated the nuclear option against Cuba.

My understanding of the Soviet side is that they were willing to remove the nuclear weapons from Cuba if America removed theirs from Turkey. Kennedy was advised he could not compromise on that for some reason, so he didn't.

Citations available upon request.