Look at that footage again, nothing about the footage would have been impossible to recreate on a set, and with miniatures. Especially with 2018 eyes. We have sets, we have scale models, we have rigs for folks to walk with wires. Pre-record as a plan B, if the feed didn't work, or some mishap happened with communications, we still needed to show the world how badass we were. I don't see the government being beyond recording footage of the moon walk and broadcasting that... then erasing all of the original footage.
I mean I would have done the same thing if we are talking about the importance of the first manned mission to the moon. And anyone that talked would be tried for treason, and likely implied bodily harm, at least.