I am like Elizabeth Warren. My family has a long-standing Native American ancestry story.
My great-great grandmother. The stories about her, first hand from my grandmother and father, were a large part of my childhood. She was a good healer who used root medicine for illnesses and "talked the fire out of a burn." She saved my father's life twice, once when he had pneumonia as an infant and once when he dumped boiling water over himself. There was a romantic, magical element to the stories but also some damn smart root medicine, the kind that grannies often knew back then. I loved the stories but my grandmother's generation was embarrassed and wanted to hide that heritage.
We traced our ancestry and that grandmother's father is a complete dead end in documents. His last name is common among the tribe we supposedly descend from. If he's not NA then he sure doesn't show up on any white census or documents.
I took a DNA test and no NA ancestry shows. My research says that's possible, given the dilution and the fact that it's my paternal line. But it's also possible it's a romantic legend with no reality.
My oldest son was born with pronounced Mongolian Spots, which show up now and then on babies of Native American ancestry. Nothing else in our ancestry search supports it and we don't have any reason to believe there were any woods colts in the mix.
So it's fraught. Lots of people have lots of stories, and they're not cut and dried. But one thing is. Donald Trump is a racist, misogynist pig who'll look for a supposed weak spot and pry at it without a hint of conscience or consideration about who he is insulting, harming or encouraging to do the same. He's a bully who counts on toadies to cheer on his nasty attacks, and if we don't all join together to stop him that's the kind of president he'll be, and we will be hated the world over for electing him.
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It's SO unfair! He pays taxes that they don't because they have a reservation! 
The newest favorite story is that my grandfather's original American ancestor was "George the Jacobite," who was captured and shipped off to the colonies by the British. That we can document. It makes watching Outlander all the more fun. 
The story was that my grandmother was 1/4 Cherokee, by her father's side. Her dad disappeared when she was very young, and reappeared once many years later, having changed his name, and told them he had found out that he had been adopted, and had gone back to the original name.
I found a group of people in the Dawes Rolls (the official government census of the "Five Civilized Tribes"
who are apparently my relatives. That family had a *lot* of kids. But the documentation about them them has a very large rubber stamp, diagonally across the page: "REJECTED". It seems that they tried to be recognized as Chickasaws, and were turned down. They also tried Choctaw, and were turned down there. They had tried Mississippi Choctaw, same result. there is no mention of Cherokee in this set of documentations, but it appears that my relatives were trying to get land that they were not entitled to. I suppose lots of family trees have scoundrels somewhere. They may have claimed Cherokee later.
Finally, I tried a DNA test. The result: no NA ancestry. It appears that the Dawes Commission was correct to reject that family (my relatives). If the family claim had been correct, n y 1/16 NA ancestry would have been obvious in a DNA test.
Elizabeth Warren has done what many of us whose family stories have done, looked at forms and thought about that smidge of background that makes you interesting and that you're proud of. Lots of our beliefs have been incorrect or surprisingly correct. Later it might take on some kind of significance we could not have imagined when we acted on that conviction. The only important thing about this whole question is how it demonstrated what a narcissistic madman will do to get what he wants.
I love the stories though. My NA ancestry is still up in the air but my DNA test DID turn up 3.1% Neanderthal! 
