Elizabeth Warren's DNA was 99.9% European. Not even 1% Native American. She said on her mother's side her parents or grandparents were Cherokee and Delaware. Genealogy research can go back two generation even five to ten generations. It could be proven easy by genealogists at least about 5 generations. Well at least she knows the truth. In the 1990s you couldn't prove your ancestry like you can do it nowadays.
Chief John Ross was only 1/8 (12%) Cherokee (and Indian blood), so his living descendants (if there are any) could be his g-g-g-g-g-g-g-grandchildren, and their percentage of Indian blood could very well be minuscule, but would that make their family history insignificant? The same would be true of the sons & daughters of the American Revolution, and yet they wave their banner proudly.