I think the whole concept of bounty hunters in FL is flawed. AFAIK, in reality bounty hunting can be quite illegal even if you're going after criminals. The only way I can see BHG working like police in every house system is if every house has contracts with them to help get rid of criminals. Which is odd because they already have police to do that. Essentially that would make them more like private investigators or something. It's strange.
Even stranger is that the BHG is a large, organized group, with its own sort of military which is at war with the Order. Usually one thinks of a bounty hunter as an independent, getting contracts from either a specific police listing, or other individual clients. Freelancer's BHG is like an organized lawful mercenary group, which apparently has been in contract with all the houses for taking care of criminals.
I honestly think the mercenary ID is more fit to carry the title of bounty hunter in most cases. But that's just me. Since I play a mercenary if the BHG demands I drop my cargo I usually don't comply, they aren't the police. Especially if they're pirate pilots, they're basically telling me to drop my bounty so they can collect on it.