"What if they used different minerals because before they mined them out, different minerals were present?"
I'd point out I didn't say that all the minerals were gone, but that the good veins were gone, surrounded by the stuff they left behind. I say that because that's how we do it now, and we do it for economic reasons that any civilization will be subject to. This is a particular pattern that I'm not aware of anyone ever observing.
I am also not aware of anyone even proposing anomalies in element distribution of things like rare earths. Rare earths aren't as rare as their name suggests as I'm sure you know, but as you go up the periodic table, you do naturally get less of them in the crust for several reasons (less created in the supernovas that created the heavy elements, and more of it sinking in the earth during the early phase). It's possible that our understanding of elemental distribution is a "just so" story created by what turns out to be artificial manipulation of the contents in the past, but given that our understanding of the processes that led to the current distribution includes a lot of astronomical observations, it'd be one heck of a "just so" story at this point. I am not aware of even a hint of an observation that requires an intelligent civilization on Earth in the past.
I'd say if you really want to have some fun, hypothesize a dinosaur civilization that attained some sort of singularity, and on the way out chose to leave behind machines that restored Earth to its "natural" state over the course of a few centuries or something, thus wiping out all traces of their presence to make way for the next civilization. It's not impossible to imagine a human singularity ending that way. Come up with some semi-compelling reason why all or at least most civilizations would tend to do that and you've got a fun premise for a sci-fi story universe. Perhaps we're not merely the second, but the dozenth. Heck, maybe we're not even the first primate.
(Another bonus "thing we clearly don't see": At the current rate of human advancement, in another couple hundred to couple thousand years, even putting aside really high-end nanotech, our primary contribution to the history of planet Earth may not be the sudden extinction of a lot of life forms, but the sudden proliferation of a lot of life forms, along with visible cross-transfer of genetic characteristics that couldn't possibly have naturally occurred. Even if the intelligent civilization completely keeled over dead, or Transcended, or whatever, the mark on the planet's genetic history would be visible quite possibly right up to the point the Sun sterilizes the Earth. We aren't there yet, but we are darned close. As much fun as a lot of people seem to derive from wringing their hands and posturing about how terrible humanity is, on a geological time scale, we may not be living in an Athropocene Extinction, but instead in the gestational phase of the Anthropocene Explosion.)