@Doug Hamilton
My guess it depends on where one is hunting East of the Mississippi River.
On private land if a hunter shoots an animal on another property by law/regulations (Tennessee, Ohio, North Carolina) the hunter must obtain permission from the property owner to recover the animal. Same goes if the hunter shoots an animal and that animal goes onto another property before expiring.
There are nice and nasty property owners. The nicest ones will let you recover the animal without questions, but don't be surprised if the landowner wants to check things out to make sure the hunter actually shot it where they claim. The nastiest landowners will tell the hunter to leave the animal lay.
Hunting public lands things can get a "little dicier" to say the least. I didn't see the guy that stole my deer, but another hunter did. Had another hunter a couple of days earlier, tried to claim he thought the deer I shot was a turkey. He started to bring his crossbow up to shoot and claim my deer. Then he saw me, my bow at the ready, and my revolver (44 mag) on my hip. He lowered his crossbow and went back to where he set up. There are many other stories of hunters having their deer taken, some where the other hunter brandished or outright pointed their gun at the hunter who actually killed the animal.
Hence why I always carry a sidearm when I go into the woods regardless of the season; archery, muzzleloader, or gun, small game, big game, waterfowl or upland bird.
There are also stories of hunters shooting cows, mules, and goats, the hunter claiming the animal was a deer.