Look at it this way. Consider a hypothetical. What if there were no other tribes in North America, except the tribes near the shores of present day Virginia. Would it be accurate to say that those tribes had a rightful claim over unoccupied lands in the Pacific Northwest of North America, simply because there is no Ocean in between?
Modern states have formal arrangements between one another recognizing established boundaries, etc. This is the basis of their claims. But if suddenly an unoccupied large continent were discovered, no single country would have a right to simply declare ownership of the entire region without some utilization of it, would they? They wouldn't have a right to say that the entire continent belongs to them because they have 3,000 settlers covering only 1/1000th of it, would they?
The American government did remove millions of Indians and relocated them to other areas. That is an historic fact. The American Government did perform acts, such as providing blankets contaminated with small pox, which by all rights can be considered the act of an invading force.
We did not stay on our side of the boarder. The American Government broke more treaties with Native Americans than did the Native Americans. The various tribes east of the Mississippi were predominately stationary. They lived in permanent villages. The American army forcibly removed them.
I believe the founding of Jamestown should be celebrated, but let's not ignore the fact that the Native peoples were not always treated with fairness.