Yeah, but as usual, that makes no sense. I mean, it being run that way before the First Uprising makes sense, but AFTERWARDS, keeping a critical line of defense under the control of a lab is just insane. A group of semi-civilian armed reploids deciding who are Mavericks? Eeeeeeee.
Besides, I could swear that I heard a council started up the Hunters, not Cain.
As for the Hunters ... I see them as a international anti-Maverick force, under the direct control of the Federation - like the UN Peacekeepers (except the Federation is obviously different from the UN, but you get my drift). I agree that it might have STARTED as a private firm, though.