No has mentioned that the initial assertion is incorrect? The US Government sent troops to remove native inhabitants. Then they gave the land away. Having an army clear the land ahead of time makes a lot of homesteading possible.
I suppose a similar sense of menace applies to some of the options on the linked inventory, but my first interpretation of the task was to think of places sufficiently remote/economically-irrelevant as to be uncontested.
This is is closer to the cycle that expansion has always taken. Groups first expand, develop economic interests, and then fight over those economic interests.
The Aztecs could have picked up tech like gunpowder and horses in a few decades and easily kept the Spanish out of their home turf, if 90% of them hadn't died from Smallpox and Maasles.
it is absolutely a different claim. The land was not empty at all, though it did have millions less people than it had had a century or two earlier. Ethnic cleansing by violence was absolutely a central part of the expansion of the US (and also New Spain before it). The only difference is the question of whether, in a violent struggle between the American peoples at their pre-smallpox population levels and arriving European settlers, the latter would have won (and with relative ease). My point/claim is that they probably would not.