I can see where this would be a problem. If people were actually hunting down and killing said character 5, 10, 20 times, it would get rather irritating. Fortunately the bounty system is such a pain in the rear for the bounty hunter to use, that it's typically more work than it's worth to file and collect a bounty.
I'm not sure if this is a good thing; in fact I'm pretty sure it's not. Ideally, the system would be set up such that an individual bounty can only be claimed once. Once the target is popped, boom, done. The bounty is fulfilled and closed; identifying and killing the same specific target more than once recognizes that the target was either not actually destroyed or (worse) acknowledges respawning, which is totally oorp.
Ideally also, the bounty hunter should not have to keep screenshot records of his kills, but apparently we need this to prevent abuse.