Why do they have television channels?? Unless they were receiving a "broadcast" from Stanley Kubrick's soundstage in Area 51 or the UK?
I guess I don't understand what you're arguing. You appear to be claiming the only possible reason to have a screen in mission control is to view fake broadcasts. As if a screen couldn't possibly be used to view genuine broadcasts, or other things going on during the mission?
In your view, were the mission control people "in" on the fakery? Were the videos of mission control faked? Was all the mission control data faked as well? It must have been faked really well for none of the people who looked at it - then or later - to realize it was all fake.
What about the contractors and engineers? They understood the design specifications, and understood they were designing something that could take humans to the moon. They tested the designs, and NASA made changes after testing. The engineering cycles don't look unusual. The design docuмents are also still available. An engineer with appropriate specialization can verify the designs are for human travel to the moonl. Which is, by the way, a lot more expensive than non-human space travel (let alone no space travel). So they designed and build vehicles capable of taking people to the moon. At which point, it's easier to, you know, just send people to the moon.
I suppose Kubrick must have insisted on filming on location.