You are right, the Kay Center doesn't allow "silencers". The official policy is no restricted firarms of any kind (suppressed, full auto, etc). The root of this policy is twofold.
First, the main reason the place is there in the first place is Hunter Eductation. It's in the deed. This by default sets the rules. You will have huge numbers of young and first time shooters. They are trying to develop basic rifle skills to pass the shooting test. A full auto right next to one of the folks to say the least would be distracting. This brings up another conflict. Since Hunter Education instills the reflex NOT to shoot at another hunter, human silouettes or human liknesses are not allowed. It's been that way for a long time.
Second, since the place is run by the LAW ENFORCEMENT wing of DWR a whole new set of legal items come up with restricted firearms. By law I cannot ask to see the paperwork. The only ones who can are certified LEO's. The vast majority of the folks with restricted firearms are good, law abiding citizens. Not all are and there have been serious problems as recently as two weeks ago. Pending a better way of handling the check, the best solution is just to politely say we're sorry, but no restricted firearms. It's not good, it's not fair, but the state is in a catch 22. No way to win.