Keeping your own crew informed and keeping the administrators informed are two different things.
No they arenít, unless youíre absolutely certain that not a single person in your crew is going to squeal. What are the odds that Nyota would have kept the secret from Spock in order to protect Kirk? Somewhere between zero and none, if not less.
Thatís the way the military works. When secrets have to be kept, they are shared only on a need-to-know basis, and sometimes not even then. Anyone who is in the military is going to have to learn to deal with the fact that their superiors donít always tell them everything.