From the various "natives" I've talked to, calling them "Americans" is roughly as offensive as calling them "Indians." It's giving them the name of their conquerors. I personally like Canada's term "First Nations," but I'm aware that US tribes have not opted for that name either.

I tend to use the term others are using, in this case I was thinking of the Pine Ridge Indian Reservation, unless it's obviously being used derogatorily. I probably should have said non-native though.