I'm with Mjolnir in this one. I thought the one thing that separated the Mercs from the BHG is the ability to operate in both sides of the law. The compensation for this is that you don't see the Houses really barring BHG, while Mercs are generally distrusted everywhere they went.
EDIT: True, there's nothing preventing a lawful from posting a bounty in another lawful. But the thing is, if the BHG goes about collecting that bounty they cannot any longer claim being lawful anymore, they're merely guns for hire and that would impact in their general reputation not only inside the House they commited the illegal act, but in the others as well. As soon as word spread out that the BHG is taking bounties against lawfuls they'd start being treated as the Mercenaires are.