A theory that adds more evidence to the 'Pearl belonged to White Diamond' theory, as well as some interesting observations about the episode, 'It Could've Been Great'.
A. Only pearl seems to know of the existence of the moon base. The others are thoroughly stumped on what to do,whereas she remembers the base. Perhaps she had been there before the revolution, as one of the diamond’s pearls (depending on which theory you support that could be either pink diamond or white diamond). If the crystal gems had know of its existence before now why hadn’t they gone their before? Be it to get information, supplies, or even to destroy it.
Amethyst also displays no knowledge of the gem’s ability to adjust to the gravity of another planet, so one can assume the crystal gems have not been off world at least since she joined them.
B. They are all together when peridot tries to get the stairs to work, with the exception of pearl. Why would the writers have them be separated for apparently no reason? Well, if you look closely the stairs only activate once pearl steps on them, not as a response to whatever thing peridot tried to do.
The system/base in general is from before the revolution (as shown by having the 4 diamond murals whereas the new homeworld insignia only has 3 diamonds represented and thus a newer/updated base would not include pink diamond) so maybe it still recognizes our pearl as a diamond’s pearl and thus allowed her to ascend the stairs. I mean why would it be called a diamond base if just any gem could get in right? Especially with the weird floaty and important looking sphere thing in this room,
(which looks like the thing white diamond is holding btw) as well as the direct diamond line: both are things that the diamonds most definitely wouldn’t want normal gems getting their hands on at most any cost. Pearls are the gems closest to their diamonds, with the exception of other diamonds so it makes sense that only diamonds and their pearls would have access to this facility. The stairs also glow white. Now this could be in correlation to what diamond the gem trying to go up the stairs belonged to/was (for example: for yellow diamond and her pearl the stairs would glow yellow, blue diamond/blue pearl they would glow blue etc.) Thus providing more evidence for the pearl belonged to white diamond theory. Or, wild thought here, they could just be stairs… You never know with this show…