That's why having Native American "blood" is not a criteria accepted by Native Americans for claims by someone of being a member of a particular tribe. It can't prove whether someone has Cherokee ancestors, or any other specific tribe. This was the point made by the spokesmen for the (real) Cherokee tribe rejecting Warren's claim.
Where Warren fails is (1) just because she has a minute drop of Native American blood, that doesn't prove she's a Cherokee and (2) the amount she does have is so minute, she has even less than the average European American who wouldn't dream of claiming to be Native American, let alone the member of a particular tribe.
It does not even do that, especially since the DNA that was compared to was not actually from anyone who was actually a native of North America. It is complete and total nonsense.
My sister spent $90 on a DNA test from ancestry.com. Thanks to my grandmothers on both our father's and our mother's side who spent years researching... we have a fairly well documented family history. The DNA test directly contradicted most of what we know about our family history. This could be either the result of an inaccurate test or an inaccurate family history. When researching the accuracy of the ancestry.com test I found that it is known to frequently be almost completely useless. Senator Warren's test which was conducted by a friend and political ally to produce a specific result is most likely less than completely useless and likely to be intentionally misleading.