Well, it certainly wouldn’t be the first time that happened, by any government. The “Weapons of Mass Destruction” lie could be described using the exact same sentence, and that wasn’t even twenty years ago.
Not defending the moon landing doubters, or conspiracy theorists in general, but: the proper response to these things isn’t to point and laugh. It’s to recognize their origins - a (often justified) loss of trust in institutions and governmental narratives - and work on addressing and fixing them.
Edit: commenters seem to be focusing on a single example, which I presented as an illustrative point for a much deeper and more important phenomenon. You’re missing the forest for the trees.