Ok let's talk about this. The "no record of gems ever coming back from the moon" thing is important. You could say it was so long ago they weren't keeping good records yet, but I don't think Sensei would be having any of that shit, gems are all autists anyway.
There's a few options, but all of them end up with Aechmea being a liar or Sensei omitting information that doesn't have anything to do with being human, or even specifics about the Lunarians' origins. Which is possible, but seems unlikely compared to the likelihood Aechmea is lying now that we know he's kept gem parts and the "gem reconstruction" could very easily be fake bits they ground up. Pre-mooncake, there was nothing special about Cairn that might have led him to keep his parts, aside from his relation to Phos. So either he's keeping all gems, or he's monitoring the earth somehow, more frequently than the blank sunspots would suggest. More likely both, since all he needs is for gems to believe that their companions have been ground up.
So if you assume Aechmea isn't lying, there's a good chance of close monitoring that factors in personal relationships, and of historical records being destroyedand you STILL don't suspect