Separate But Equal

I don't think it's accurate to say that the Americans colonized the Indians the way that the Spanish, French, and English colonized the Indians.  Indeed, one of the bones of contention that led to the American Revolution was the British attempt to keep the American colonists from spreading their influence west of the Alleghenies. The British had their 13 White American colonies along the Atlantic coast, and that's where they wanted them to stay.  The British presence in the Northwest Territory was all about the fur trade with the Indians, and they did not want anybody to disrupt that by establishing permanent settlements in the region.  When Americans later settled that territory, all they wanted was the land, without a lot of Indians on it.  When the English ceded the territory to the Americans after the war, one of the conditions was that the Indians' right of occupancy be preserved, and the Americans had to figure out a way to weasel out of the deal without giving the British an excuse to try to take back the land like they did in the War of 1812.

Truth be known, the Indians never really owned the land.  According to their own traditions, the land was owned by the Great Spirit, who graciously allowed the Indians to live on it.  Since the Kings of France and England ruled "by the grace of God", and since both kings respected the Indians' right of occupancy, things didn't change all that much.  When France ceded the land to England, and when England subsequently ceded the land to the Americans, it was the Indians' right of occupancy that was preserved, not their title of ownership.  With some difficulty, the Americans eventually persuaded the Indians to give up their right of occupancy in exchange for some tools, trinkets, free medical care, free hunting and fishing, and exclusive rights to any casino operations that might be established in the future.  There is no evidence, however, that the Great Spirit ever signed off on the deal, which is why Northern Michigan is called "God's Country" even unto this day.