The conspiracy that Fox missed (well, they do miss a lot) is called by its adherents "Alternative 3". Its promoters are shadowy individuals like Bill Cooper, a formal US Naval Briefing Team member with access to state secrets, who claims that an advanced American space presence is a reality. In Behold a Pale Horse, he reports that "A moon base, Luna, was photographed by the Lunar Orbiter and filmed by Apollo astronauts... I can say that 'Alternative 003' (a British TV documentary on this subject) is at least 70% true from my own knowledge and the knowledge of my sources."
The GRAIL mission determined the internal structure of the Moon in great detail for nine months during 2012. Armed with this the new information, GRAIL astronomers were able to redefine the sizes of the largest impact basins on the lunar surface.
In fact, it may be much more reasonable to suppose that the American government's real capabilities in space exceed anything we have heard about, or can easily believe.