In principle, the chiefs' argument is right, that nations decide who is one of them. It's understandable they defend her because she's been part of so many important decisions and cases. Quite a few racists who don't give a damn about NDN causes will and are jumping on this to discredit NDN causes and undermine legal decisions.
But the fault falls on her for what seems pretty clear lying about who she is. She could have accomplished the same things as an ally, and her lying undermines everything she's done. This is different from the Margaret Noodin case, where she seems to have actually believed herself Native. METL even seems to have altered her appearance, from wavy even frizzy reddish brown hair as a teen to straightened darker hair.
From an academic, legal, and govt standard, her falsified resume and honors matter much more than her identity claims. That may be enough to force her out of her positions. Does anyone see any reason not to place her under Frauds?