Oh cool, so even though it's an orbital installation populated almost entirely by their ships, it doesn't actually hurt them if someone goes on a massacre there? Fantastic.You can't hurt anarchy will violence. BH fights an anarchy directly by handing in bonds, and boost other factions at the same time.
Bear in mind not all bases are suitable for a good kicking- my advice is scout them and see what can be blown up- some are just boxes with streetlamps
I can see how there'd be salt if blowing up ships in lawless areas still counted as a murder for influence. An anarchy with a large orbital would be untouchable as you could just hang around it with smart rounds and blow up anything that tried to pass through the slot that belonged to any other faction in the system, for absolutely no consequences other than rep.