Because of the differing manner in which Eastern and Western Cherokees trace their genealogy and blood quantum (Eastern is through the maternal line, Western is through both the paternal and maternal lines), it was possible to slip through this anomaly, and hope that nobody would ever call out Elizabeth Warren on it. Almost all the “faux Indians” claim to be some degree of Cherokee ancestry, as it is one of the harder ones to disprove, because of this dichotomy. And besides, “Cherokee” sounds so mainstream Native American. The very word “Cherokee” is not even their own language, it was the Creek Indian word for “people who live in caves”.
That covers literally millions of Americas alive today. The Cherokee could see that their only chances for survival as a people included intermarriage with the dominant tribe (whites) and sought these alliances for practical as well as political reasons at the time. The Cherokee wore white man's clothes and learned the white man's law during this time up until the 1836 Trail of Tears expulsion.
The fact that Warren could not clear even this fairly low hurdle makes her fake claim all the more repugnant.