If they had the time to go through the chain of command and reach a measured, rational decision, perhaps; but it's quite possible that a crew manning a missile

If they had the time to go through the chain of command and reach a measured, rational decision, perhaps; but it's quite possible that a crew manning a missile defence platform had only a few seconds to decide on a course of action, and went with "better safe than sorry" without considering whether it even was something that could break up.