I think that she actually believed it at the time.
I understand about family legends. Apparently that family did tell themselves and their children (falsely, as it turned out) that they had "an Indian in the woodpile" somewhere in earlier times. There is a strong legend of that sort in my first husband's family, which if true would make my daughter 1/16 Cherokee --- a whole lot more Indian than the 1/1056 Latino DNA Warren is claiming. But the great-great-grandmother, whom I actually saw alive at the end of her life, never would tell who did the deed --- got her pregnant with the illegitimate boy. His sons did look pretty Indian, I agree.
BUT ------- nobody ever TRADED on this dubious idea, which could not be proven, and no claim of any kind was made publicly --- and you better believe none of the people involved ever called themselves Indian on any form to get some sort of preferential treatment! That would be fraud and immoral. The idea was not proven and could not be proven any more than Warren's claim, though that family's idea about what happened was a lot more recent and more compelling than Warren's.
First you have to know what the family geneology actually IS --- know when and who. Second, it needs to be more than just some story that a batty aunt spins on Thanksgiving about something she imagines happened 200 years ago. Something that might have happened 200 years ago does not make anyone an Indian. Warren never bothered to prove her claim: she just used it to get preferred entry into Harvard and state legal bars. That's about as bad corruption as you can go. It's completely unacceptable.
I don't care what she believed --- she didn't prove it and she used this unproven tale to benefit herself. And she was dead wrong all along.