Uh, you might want to read a bit about the settlement history of the Sooner State because this is exactly what happened. The US government moved Native people from their ancestral lands to "Indian Territory" in what is today Oklahoma. Then the US reneged on their treaties again by opening land here to white settlers through the "Land Runs". The result? Tens of thousands of white people rushed into Indian Territory to stake their claims literally overnight. This created a mix of white and Native folks living alongside each other and lots of opportunities for intermingling.
Today, some of the whitest of white people in Oklahoma have legit Native ancestry, just like Warren claimed she did (and indeed does have). I'm talking about blonde-haired, blue-eyed people who are card-carrying members of their affiliated tribes. This is a real thing.
BTW, I'm often saddened to meet Mohawks, Kickapoo, Lenape and other people whose ancestors lived far away but are now exiled to Oklahoma. For example, I've got a Kickapoo student with whom I work and his people were from the Great Lakes. The climate, vegetation, wildlife, etc. are so dramatically different here compared to where his people are actually from there is likely little of his cultural traditions that might have survived to this point that make any sense to him.