Especially with an element of "I might personally get blown up" involved.
They probably had second thoughts, but they got confirmation that contact 4474 was descending rapidly.
0: https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#Averted_n...
2. "X did not happen" does not mean "Y was not a factor in X". The "about to get blown up" factor was part of the reason the Cuban missile crisis happened; it's also probably part of the resolution.