I've read this idea before and just came across it again in Zinn's "A People's History of the United States."
"One fact disturbed: whites would run off to join Indian tribes, or would be captured in battle and brought up among the Indians, and when this happened the whites, given a chance to leave, chose to stay in Indian culture. Indians, having the choice, almost never decided to join the whites."
How accurate is this?
Not to discourage further answers, but check out this thread from seven months ago that was prompted by a New York Times article and a TIL post asking a similar question.