If the Americas were uninhabited when the Paleo-Indians arrived, "colonization" isn't the right word. The Paleo-Indians didn't colonize the land, they settled it.
Here's the dictionary definition of "colony":
Sorry, but the length of time Indians have lived here does make them "native." When your origin is so ancient that it's lost in the mists of history, you're essentially indigenous or native. The distinction between coming here 10,000 or 20,000 or 50,000 years ago and originating here is infinitesimal and irrelevant.
Again, here's the dictionary definition of "native" that applies:
For more on the subject, see Kennewick Man, Captain Picard, and Political Correctness.
Below: The first Americans.