If you are responsible for building the industry that designs and builds nuclear submarines that carry nuclear missiles, you had better make sure that those submarines and their crews can handle chaos monkeys.

Also, Rickover was Congress's favorite admiral. They forced the Navy to promote him. I'm pretty sure they made sure that the laws were to his liking.

Rickover was the sort of person who had the technical expertise, gumption, and charisma to get away with this. It's worth reading up on this amazing individual, who made navy's nuclear reactors so safe, and led the creation of nuclear reactor expertise within the navy.

Also, if you're not confident enough in your nuclear reactor to apply chaos monkey techniques, you shouldn't be engineering nuclear reactors.

In general, one would hope that a nuclear system is designed such that the problem can easily be corrected if a single button or lever is accidentally pressed. It would be quite a terrible system if you could e.g. trigger a meltdown with just one action.

A reactor scram is basically just an emergency shutdown. If I were a nuclear engineer, it might give me a heart attack to hear the scram alarms, but I would be plenty happy knowing the scram works.