Having unlocked this recently, I can confirm that a Dark Zone being occupied will not interfere with the Achievement. While in an occupied Dark Zone you are automatically rogue, you simply need to attack another player until you are declared as disavowed and the timer appears at the top of your screen.
This is easy to boost with a friend, just enter each Dark Zone, press and hold the back button to go rogue, then kill your boosting partner to be disavowed from The Division. Your partner respawns at a nearby location, and kills you before other players get the chance. Repeat this at all three Dark Zones and the Achievement is yours.