I've participated in simulations in the backrooms in the MCC, both in the old Payload MPSR and in the new(er) POCC. While there are some parts of the simulation that are very realistic, there are always details that are different from the real thing, and overall the simulation can always be distinguished from the real thing.
Granted, mine were Shuttle-era simulations, but that only means with information technology considerably more advanced than Apollo, you still can't fool the controllers and backroom guys. Anybody who claims so is simply ignorant of how mission operations and the underlying technology work and assumes wrongly that everyone else is as dumb as they are.
I also second the controller's remarks about the tracking networks and the large numbers of personnel involved in them, from countries around the world. They tracked Apollo missions to, from, and around the Moon, and commanded and received telemetry from the ALSEP experiments for the better part of eight years. Hoax believers claiming that such operations and science data could be faked are ignorant and incapable nobodies claiming that everyone else is as inept as they are. Fortunately, that's not the case, but I feel kind of sorry for them.