There's a recurring phenomenon across many societies called "hypodescent", the automatic assignment of children of a mixed union to the subordinate group. This practice developed in America back in the 1600s, hand-in-hand with slavery, and it led to the widespread informal and in some cases formal use of the "one-drop rule". To the extent that people have been infected by that thought process, and to the extent that they see American Indians as a low-status ethnicity, for them to infer that someone with an American Indian great**N-grandparent counts as an American Indian can be automatic, the fact that her percentage doesn't really justify it notwithstanding.She used these "family stories" to further her career. The DNA test gives a very tiny percentage as being Indian, so it does not really justify calling herself "American Indian" like she did on her Texas bar registration card.
Face it, she lied about her ancestry.
So Ms. Warren's statement isn't evidence of her lying so much as evidence of her being easily influenced by mindless memes prevalent in whichever poorly-reasoning subcultures she gets exposed to. Which, come to think of it, could also account for another statement she made.
It occurs to me her family might not even have known the true situation. Think about the one-drop rule applied generation after generation--all that gets passed down in family history is "American Indian", not the percentage. More than a couple of generations back people don't know the actual ratio and from the one-drop it's thought to be 100%.