I hit a guys chicken going though NM, I though about pulling around and yelling at him since it looked like he purposely scared it into the road when I was driving by. He started yelling and screaming and flipped out. At that point I remembered all of the stories and got the hell out of the res land.
You can still be at fault for hitting live stock when not on reservation land. It has to do with whether or not you are on open range or not.