I agree that "someone else's land" is a bit much.
Saying that "North American Aborigines lived outside the republic" is a bit misleading, because it insinuates that they weren't interested in assimilating, and becoming a part of that struggling, triumphing mass of people that identified as Americans at that time.
More truthfully, leading up to the times when they were forcibly relocated to reservations, they were never allowed in, for the same reasons that black residents of the US had a tough time in those years: the world around them was quite racist and (especially in the case of indians) kleptomaniac.
In fact, many Native Americans tried to assimilate; I remember reading about one enterprising native gent in the early 1800s who had made himself quite rich from trade, had a mansion, the whole nine yards ... until the day came when his town wanted his stuff. So they took it, because America was in large part founded on the notion of repeatedly taking stuff that the natives considered their property.
Acknowledging the massive wrongs committed by this country against those peoples isn't necessarily a bad thing, but I agree with you that we need to be realistic about what conclusions we draw from it. Yes, the United States stole stuff from the indians. No, we're not going to now consider dispossessing the current owners of that stuff; that's akin to, say, questioning the rightness of the origins of modern-day Israel. There's a state there now, so it's moot.