Could the “fake” moon rock possibly be the real thing?
You are right that there is some kind of shared similarities of the material of which the Moon is made and the Earth is made. We find enough similarities that once upon a time major theories thought the Moon had broken away from the Earth. However, there are enough differences in material as well to rule out as a single cause/source of the Moon. So, current thinking is that a smaller planetesimal (think large asteroid) hit the Earth breaking off a lot of material. The material, some from the proto-moon (and thus different) and some from the Earth (and thus the same) combined to form the Moon. At the same time, a small fraction of the proto-moon’s material became absorbed in the still-hot-and-now-reforming Earth. This clip from “The Universe” series on the History Channel talks about it.