Actually, you brought up a very good point. First, you and CatParty are absolutely right. But let me elaborate a skosh.
Historically I've considered CON a sub-branch of the Rat King, since while the likes of Quinn sure as shit isn't directly in it, a shitload of people involved in CON are. Historically, I've always thought that this was a case of the obvious, since these morons tend to get into circlejerks as easily as breathing. Pretty much every accusation of collusion with them in the past has panned out, after all.
All of which, however, is ruined by a brain-dead typo that I'm seriously pissed at myself for missing despite the fact that I've talked about it like fifty times: Quinn, Harper, et al hedged all these idiots out. They added them to the blocklists, they actively avoid them like the cancer-ridden shitheels they are, and all evidence is that any connections they used to have with them are gone now, regardless of whether or not they originally associated with them. Looking closer at it, one can't really blame them considering.
So in other words, the argument could be made that they may have been technically Rat King-related once? Like 2 years ago? But they sure as hell aren't now, and haven't been in quite some time.
With that in mind, it's been fucking dumb of me to consider CON itself its own branch, but things really came even further into perspective when I was trying to put together a sort of flow chart map for just one section of the Rat King. I was trying to see just how much of a clusterfuck it could get, so the idea was to lock down a few examples and see how they scatter out. When I did so, however, I finally realized the obvious you bastards were trying to smack me with all along: Of the various cows that extend out from what I considered the "CON Branch," basically ALL OF THEM are there anyway if you cut Crash Override out of the picture entirely, from Jake Alley to David Gallant.
TL;DR: What I thought was its own branch really wasn't. At least not currently. I fucked up, and I will own that, and I thank you guys for pointing it the fuck out.