Yeah, I didn't list them because I didn't think they really fit the first two criteria. Sure, they're a mysterious organization who KNOWS THINGS!! THINGS THEY SHOULDN'T!!, but it seems like a stretch to say that they know the Vongola "better than anyone." And they've been neutral parties in every single appearance before this, so I can't picture them being disappointed in the Vongola, let alone taking sides with the Shimon family against them.

I guess it's still a possibility, though; there's a lot we don't know about them, after all.