It's ok, you can take the foil hat off. The broadcast from the moon was relayed live to TV stations across the world. The tapes they're talking about were just NASA's recordings of that direct broadcast. So there never was any opportunity for the tapes to be edited like that, because they didn't sit in the chain between the cameras on the moon and the broadcasts everyone saw on their TVs. Fortunately other news organisations (and probably governments) also taped the broadcast as well, hence we still have recordings available.
In fact, it was technologically impossible to record the entire live broadcast on a single tape because tapes with enough capacity didn't exist until many years later. Therefore a faked broadcast from tapes would have had visible transitions as they switched from tape to tape. These transitions would have been visible on the taped copies of the broadcast which the currently available recordings derive from.