I was reading in Smithsonian magazine that all Bison have some cow genes. So there aren't really any pure ones left that they could find. And even if they could find them, there are so few, as you mentioned they would end up inbreeding quite quickly. I thought the same was true for Amherst, but since they aren't scientifically/culturally significant as bison, there's no genetic testing for those. And people who have "pure" ones, might not really have them (honestly misinformed) or might advertise them as "pure" even knowing they are not just to get better sales (dishonestly misinforming).
But again, those are different because the impurity comes from hybridization with different species.
We're talking about the same species, just different varieties developed by selective breeding of spontaneous color mutations and other characteristics like size.