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."
This cycle has been appropriately named the 'dark moon'. The cycle from one dark moon to the next is called a lunation and an average lunation calculates at about 29 days, 12 hours, 44 minutes and 3 seconds (roughly) To be fair, it does deviate in relation to the moons erratic orbit patterns and is affected by the gravity conflict between the sun and the moon.
Earlier infrared data did not have sufficient resolution to separate MK 2 from Makemake's veiling glare. The astronomers' reanalysis, however, based on the more recent HST observations, indicates that much of the warmer surface spotted earlier in infrared light may simply be the dark surface of the companion MK 2.