I've played Red Dead Redemption for a while, my favorite job is Bounty Hunting. Now, you can either hunt them down, lasso them, and bring them to jail - or kill them. I never really thought deeply about how killing the bounty worked. You would loot their corpse for proof, then bring back the evidence and claim your reward.
After watching Hell on Wheels, a western television show on AMC, I made the connection.
John Marston scalps the bounty. I'm sure Rockstar had their reasons, but the game just doesn't come right out and say it. This is by far the only way I can think that John can retrieve proof from the corpse, and deliver it to the lawmen. He cuts of their scalp and hair with his Hunting Knife, and brings it back, and claims his reward.