You are correct in assuming that the Yakuza are now a part of this faction. As for the incident you describe... can you elaborate a bit? What exactly counts as "steamrolling"? A Raba and a pair of Black Dragons, or a full armada?
Tau-23 is perfectly legitimate operating turf, by the way. It's 50k and two lanes from Kabukicho, which makes it roughly as far away from our primary base as the Honshu system. We've been sending piracy squads (1-3 people) in there for the past few months, and the denizens of Tau-23 have responded with a plethora of bounties. If you'd like more details on why it's okay for the Hogosha to act in Tau-23, I answered that question a few pages back in this thread, the reasons still apply.