NASA had a satellite named TETR-A that could send test data simulating a real Apollo spacecraft's information.
Also as Huston receives it's data from satellite dishes around the world, that data could be anything coming from anywhere, including inside mission control itself.
Would this have been doable in 1969? Absolutely, as a former computer guy working for AT&T Network Systems, I myself am qualified to answer this question.
Someone in the control room could not be absolutely sure where that data was coming from.
The guy sitting at the console would not even think of questioning it.
Also, maybe the guy at the console was an insider.
Or, maybe the guy at the console was told to keep hush if they saw anything out of the ordinary, and immediately report such to a certain person.
MOON FAKER - TETR-A VIDEO