I'm sorry, the weak cause? BC was planning to jump in with CoJ on a curbstomp with an already involved 57th, not because their allies were involved, but because they perceived there was some sort of feud?
Also, I think this puts it well
Well, BC got their war.
Look at it this way, the 57th helped you save your own honor. You wanted the war, now you get it on less pathetic terms.