Interesting, I didn't realize that region was empty. I dimly recall something about the area of the SouthWest that the Comanches occupied said that they themselves were new to the area and a breakaway tribe from another nation. So, the empty land idea seems to coincide.
I even read once where there are to this day, people of Mexican or Spanish origin living in the American South West that always lived there and have no family ties to Mexico. I think there's even a name for that group (ethnicity?). But their lineage has been in America longer than most white Europeans, they're in the areas like Texas, Arizona and New Mexico, some may have gone as far north as Colorado.
I once read something similar about South Africa. An old book seemed to indicate that when the Huguenots (or the Dutch, I forget who was first) arrived that land was empty too. Of course, that idea wouldn't wash today. There can't be European settlers without genocide.
Aha, I was right! I just did a quick Google search about South Africa being empty, apparently it's now a long discredited "myth" called the "Vacant Land Theory".

I'll file that one away in the "suspect" folder, I'm no expert, but it sure seems pretty convenient in today's ideological climate. Although, I have no doubt that European settlers would have been just as awful to native populations as the native populations would have been to them had they had the guns.