late edit: DISCLAIMER: The pictured map is not actually a representation of the territories before colonisation. It's a hypothetical map of what countries there might have been had the continent not been colonised, thus all the names and borders are fictional and have never existed.
For good actual maps, check out native-land.ca.
My wife's family is Appalachian (WV) and what I've distilled is that anyone who could tan at all (ie not completely ghostly Scotch-Irish) was told "well that must be indian blood in you!"
And then later they tell their grandkids "Your uncle roy was part-cherokee!"
Then those kids grow up and tell their kids, "Your great uncle Roy's grandma was Tenskwatawa's sister!"
It's all just a bad game of telephone with foggy memories and no real fact-checking.