It's a matter of public health. Think about it: if you were bitten by a strange dog, how would you feel about a stanger assuring you that he'd given the dog a rabies shot? You would have no way of knowing whether the vaccine was still good, whether the dose was correct--or for that matter, whether he actually gave the dog a shot or not.

Granted, it is much cheaper to give your dog a rabies shot yourself--unless you come to the shelter's monthly shot clinic and figure in all the other protection for your dog (or cat). And remember, it doesn't "count" unless the rabies shot is given by a veterinarian.