Let's follow the logic here.
Aliens come from distances vast and empty through endless wastes of space and time...
And camp out on a chunk of basalt about 400,000km away. That's airless, goes from 120C to -150C, bombarded by cosmic rays, and far enough down a gravity well that it's difficult to leave.
Oh, and it's surface weathering is so non-existent that any record of any physical activity will stay essentially until our sun goes all red and gianty and eats us all.
We can't see any of their fantastic stuff from Earth, so they must be on the dark side. But if they're on the dark side, what would be the point? They can't watch us from there, they're energetically as far away as lots of asteroids which have a smaller gravity well and more abundant interesting rocks to use for stuff. And hell, we probably wouldn't even notice if a bunch of them got busted up and used for stuff.
Oh, and oops! We've mapped the whole surface repeatedly by several different nations. Are they all "in" on it?
Now, I'm not one to say that it makes no sense, therefore there must be nothing there, except in this case there actually is zero evidence in my opinion AND it makes no sense. We should be looking at the Lagrange points. That's where I'd go and just sit there for free. L1 wouldn't make sense because you'd be silhouetted by the sun. L2's pretty close, and we'd probably see it quickly. L3 would be pointless because the Sun would be in the way and they couldn't see us. L4 & L5 are big regions filled with Trojan asteroids if they want minerals to use for some reason, and far enough away that we probably wouldn't notice them.
I mean I know it's mysterious and romantic and all, but even manned bases on the moon as "way stations" for Mars don't even make sense in my opinion.
I'm not saying we shouldn't put a manned base on the moon and go all Space: 1999 on it. Hell, sign me up. But do it for the science, the helium-3, and as a rescue boat in case our planet goes all melty from a giant asteroid we can do zero about.