Compromised nav beacons are definitely not exclusive to anarchy systems. I had been camped out at Ross 773 for a while which is not an anarchy. These beacons seem to not allow a distress call to authority ships, making them ideal for pirates and smugglers.
Based on that, it's a good assumption that this occurs when a criminal/pirate faction has gained a lot of influence in a system, but is not in control (in the case where the system is not anarchy). The civil war status (when one of the warring factions is pirate/criminal) may have to do with this as well. All of this needs verification.
FYI I am an xb1 player, so no promises that this holds true for PC.
Awesome place to farm. If you're good enough at combat to take down elite level NPCs, you are talking about accumulating one-mil+ credits in an hour. Don't be shy about retreating though, as these are not your typical shieldless sidewinder pilots. For me, when my shields drop on my Fed Assault Ship, I begin to consider escape. If my hull hits 60% at any point, I'm out to repair and cash in. Don't bring cargo!
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It should be noted that if you attack a "clean" ship (and the system is not anarchy) you will get a bounty! Even though authorities will not come, there are still bounty hunters. I've seen elite anacondas in a pack of three bounty hunting, so use caution.