She has never claimed to be. This entire furor has been created because she filled in a form from her employer listing all of her known ancestry, including native American. She never claimed to be more than what her DNA test proves, and already had the job.
Ask me and I will say I am half Norman English and the rest is mostly Lithuanian Jew, but family rumour has it one of my great grandmothers was raped by a Cossack. I could claim to be part Russian. Ancestry is not something you choose, and being honest about it is nothing to be criticized for. Anybody who thinks differently is, with respect, being a complete fool.