One of the functions of the zampolit was to be a pain in the @$$, I mean enforce the political orthodoxy within the military unit. In this case the submarine. One of the other functions was also launch order authentication. The go order would travel through two channels, the military command and the political directorate. So the submarine commander and the zampolit would receive the SIOP order through separate channels, or at least separate messages with different encryption. Supposedly provided some redundancy. Then again anything could be broken.
As for the KGB on board the boat not knowing about the failsafes on the warheads, it seems likely. The "atomic cities" were pretty much closed and isolated, those working in those facilities rarely permitted to travel or have contact outside.
It would be highly likely the guys on the boat wouldn't know about the failsafes. But I bet the guys who planned the operation, supposedly including the Director of the KGB and his staff, would have known of them.