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."
Several possibilities could provide an answer as to why the moon would have charcoal-black surface patches, even though it is circling a dwarf planet that is as bright as freshly fallen snow. One theory that has been suggested proposes that, unlike larger objects such as Makemake, its own little companion moon is so small that it cannot gravitationally keep a grip onto a bright and icy crust, which then sublimates, undergoing a sea-change from solid to gas under the melting influence of warming sunlight. This would make the little moon akin to comets and other KBOs, many of which are well-coated with very dark material.