oh boy, and here i thought you had atleast a vague idea of what was going on
lets clear a few things up
1. regardless of if the Yakuza approved of this girls rape/torture in particular, the fact is that it happened
2. IF people tried to ACT AGAINST the rapists/assaulters, even IF the rapists,ect in questions were the ones who instigated it all, its still considered "fucking with them", therefore Yakuza => "Defending Honor"/"Help fellow member" mode
3. now think about it logically, the Yakuza, or all organized crime if you will, relys on image and shows of cunning, force, and manipulation and distain for the law
now here we can see two possibilities
1. Yakuza back up this kid: adds more intimidation factor to the Yakuza image
2. Yakuza DON'T back up this kid (who's connection to the Yakuza was already known)
makes them look like a bunch of pussies who won't go that extra step to break the law, bad no matter HOW you look at it.
and as for Yakuza as a whole
their policies are (in a nutshell): 1.avoid things which bring unwanted attention towards the group.