I think you're mixing up two different things - government type and security level.
Indeed. This is exampled when you see system security flying around in an 'Anarchy' system; just because there are a bunch of rent-a-cops running around, doesn't indicate there's a central governance. The system security level, and the factional government types, are not interdependent. This isn't well understood and I possibly am not entirely 100% correct either, here. It's still a bit of an "exercise for the reader" to work out exactly how it all functions.
But my understanding, in short, is that Anarchy reflects a lack of official governance for a system; it also supposed to denote the relative security risk (if only the game actually used this more). System outposts and stations may be 'controlled' by a faction, but this doesn't mean there's a central governance, or controlling faction for the entire system.
It's not that it's Anarchy-controlled; because that's an oxymoron, it's because there
is no central governance; it's just loose political structures cohabiting the same system. This is why a player faction can be a controlling faction (this is really only relevant for stations and outposts, as we known) and yet be in an Anarchy system. They aren't mutually exclusive.
Folks often confuse this and then expect crime to be policed in Anarchy, because there are Corporate or other factions and presume this should extend to global crime prosecution for the system; which ignores that factions typically won't give a crap unless you're smashing their reputation, and all that does is sends your reputation spiraling (which of course is leveraged by BGS players).
It's only when you're in a system that has true central governance (eg independent, or major power aligned) that the rule of law is technically policed. I say technically, because the AI is truely incapable of holding criminals to account unless in vast number, or at a station. So.. there's that. Anyhoo.
Frontier, though, does a really poor job of describing this to commanders; it's an endless source of confusion. :<