There's another reason some people -- especially in the South -- claim remote Native ancestry. It's to cover up remote African ancestry.

Many people in the South from old settler families (people who came prior to USA independence or shortly after ) have remote African ancestry. This occurs most frequently in the Carolinas, Louisiana, and some parts of Appalachia. Especially prior to Bacon's Rebellion (1676), enslaved Africans and indentured servants from Europe sometimes mingled. (In the wake of Bacon's Rebellion the first segregation laws were passed.) Descendants of these people claimed to be "part Indian" to account for their slightly darker skin. It was better to claim relations with the "Noble Indian" than to come under the "One Drop" rule and lose basic civil rights or even be kidnapped into slavery. In doing so, they deny and disrespect their African ancestors while misappropriating and disrespecting Natives. Of course, some people from old settler families have some remote Native ancestry also, but in most instances the greater percentage -- indicating more recent ancestry -- is African.

This may apply to Elizabeth Warren's family. It is said that her mother had to elope because her in-laws to be disapproved of her off-white appearance, said to be "part Indian." When Warren released her DNA results, she highlighted the tiny percentage of Native DNA. She didn't say anything about African DNA but I'd guess there was more of that. Look closely at photos of her face and see what you see.