Well as she has answered... it was in family "lore" that they are part Native American. As far as they traced back they can find no trace. She is now saying she had no idea that Harvard was carrying her on the roles as a Native American as opposed to the white person she is.
By the same standard she's not fully European-blooded owing to a lack of lore in that direction too.
I'd say unless it affects anyone in some material manner, we each have a right to our own identity.
Unless you can prove otherwise (not everyone can trace their family tree for various reasons) you must accept that she could be anything if she can't trace her family tree. So if she thinks it's native, unless there is some material or legal repercussion, let he say what she believes.
Hey I'm Native American too if you want to look at it that way.
However if I check of "Native American" I better darn well prove I have "American Indian" blood in my veins or it is fraud. Native-Americans have minority status and there are benefits through Affirmative Action if they want to use them.
Harvard used her family lore to say they have a Native American in their Law Faculty which is the EXACT equivalent of a Canada's First Nation people. They used it to show diversity among their faculty when there is none.
Certainly if she or they are using it to fulfil some legal requirement, then definitely she must prove it. In other words, she can call herself native if she wants to, but not on any official document.