The easiest way to shed it is to take a DNA test and release the results. The fact that she hasn't suggests maybe she has already and the results weren't what she expected.
I forget if Warren was ever specific about how many generations back her alleged Native American ancestor sits on her family tree. If it's like ~10 or more generations back, and all of her other ancestors are European, then there's a chance that it wouldn't show up on a DNA test. But my recollection is that she implied a more recent connection than that.
