No one is that dumb. Her, her parents, they are white. A white household with a white culture. If they tell stories about great grandma cherokee indian whoever that's amazing, but it still doesn't make you Native American. Not on a level where you add it to your brand to all relevant parties and institutions. I shouldn't start saying I am hispanic at work because great uncle Jose may have been according to my dad. If you say it in passing or to friends in conversation that's one thing, but if you are advertising yourself as Native American on any relevant level because you think you have an ancestor, and claim to never have once known it was referenced in any way after the fact to all the relevant parties you yourself promoted it too, that sounds incredibly dubious.
Either she is incredibly stupid and naive, or she purposely overplayed her "heritage" to potentially boost her opportunities. Whichever it was points me towards a different candidate. We have enough stupid and/or manipulative people around. No need to add one more.