Thanks for the example. First, this conspiracy theory charges that government lied about the successful moon landing to the point of creating the illusion on tv, not that they're simply hiding a natural fact not of their creation. That goes back to the difference between a cover up and discouraging discovery.
Secondly, yes, I believe we landed on the moon. But it didn't really matter beyond the boost to patriotism, which died anyway with the guy who made it all happen: JFK. The #1 reason of the Space Race was to catch up and surpass Soviet rocket technology after Sputnik, which caught U.S. intelligence by surprise, because we couldn't afford them having an advantage in the delivery of ICBMs. We didn't need to walk on the moon to do that.
Moreover, that silly controversy is a joke within government. It highlights, yet again, how the public is clueless, why they should remain that way, and how easy it is to keep them that way. Had government demanded to spend billions on ICBMs technological development in order to vaporize the Soviets and Chinese, it would have had a more difficult time passing Congress. Slick talk it as a benefit to mankind, and it passes with ease.
A modern version of that is allowing the public (from their own imaginations) to believe that those "tic tacs" are coming from extraterrestrials instead of our own defense industries.