The supposed "native american" fighting style of "Tushkama" is not backed up by any sort of historical evidence for it's existence.

In other words, it appears to be Bullshido. The "grandmaster" is capitalizing on the "native mystique" in a blatant show of culture thievery and exploitative exoticism.

All available evidence suggests that native american cultures had no formalized unarmed martial arts, but rather combat sports.