The US's version was written by the white house's journalist. It is not objective and lots has been refuted from calls leaked by the soviets after the fact, and a few of the advisors too.
TruTV/Adam Ruins Everything has a take on it [0] (not saying that's the objective history but they raise some eyebrows).
Some facts we do know though:
1. JFK rode on an anti-communist wave to beat his opponent into office
2. The US moved missiles first
3. The military was following orders from the top
[0] https://www.youtube.com/watch?v=k5wc9V7ggVg
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EDIT: on some reflection, I think I actually just proved your point. If that was just left to the military then cooler heads may not have prevailed