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.
The moon's orbit. The moon's orbit is not on the same plane as the earth's orbit around the sun. If it were, every time we had a new moon we would have a solar eclipse, and every time we had a full moon we would have a lunar eclipse. Instead, the moon travels in a track that goes well above and well below the earth. Still, on occasion it will travel in between the sun and the earth and in this case, there will be an eclipse.