I understand the previous commenters' arguments regarding the tangled history of Native enrollment, the effects of miscegenation, etc, but those rebuttals don't really address the fundamental question of how those realities enabled Warren to contribute to the heterogeneity at HLS. Additionally, they're hewing disturbingly close to the reductiveness of, "Humanity orginated in Africa, so we're all African-American."
If Warren does have a distant Cherokee ancestor in the recesses of her family tree, that's wonderful, but what does that fact mean if it's totally separated from exposure to customs, traditions, culture, and so forth? Warren may be "proud" enough to claim her tenuous connection to a hypothetical heritage, but evidently she wasn't so proud that she educated herself on the points of culture unique to that ancestry.
Also, the notion that because one vaguely "feels" like a certain race, one automatically is that race is just illogical in the context of an America that has a complex and often shameful history with respect to skin color. To deny that aesthetics have no relevance to questions of ethnicity and self-identifying in certain contexts (the department of labor and professional directories are implicitly equal opportunity initiatives) is to essentially negate, for example, the prejudicial undertones of Birtherism. How do you know that Donald Trump doesn't "feel" black or somehow believes that he has a black ancestor, and, consequently, who are you to say his demands for Obama's long form birth certificate are racist? That's where ethnicity-as-an-abstruct-construct leave us.