Most of the time when we see The PS with Rhue, Rhue is looking at him. Most who believe Rhue is the PS write of these events with the fact that the story is played out in Rhue's view. BUT, episode one we frequently see the PS with Rhue, and Rhue is not looking at him. So, I think this pretty much writes off the theory that Rhue is the PS.
Personally, I think the PS is following Rhue to get his body back - and is waiting for a certain something to happen so that he can. In the jail cell in episode 5, the PS frees Rhue from the cell and quickly runs off. Rhue then steps outside to find the PS has vanished, and then retrieves his sword from the chest. Maybe the PS does live inside Rhue's sword as some theories suggest, and is able to come in and out at will...
Rhue absorbed an aura without his sword in episode 4, so it can't be his sword that gives him this ability. Then Rhue is injected with the formula and in that period it seems that Rhue went crazy and killed everyone. Maybe the PS took over when Rhue's aura was seperated from his body, but was unable to keep it's hold.
The PS may be an aura that Rhue absorbed. Possibly Midain or Jeruh? This would explain why Gaius thinks he is this PS, and also why he believes his aura is muddled in episode 2.
Maybe the PS's aura is stronger than most, and is able to seperate itself from Rhue at points, but not for long. Maybe it can store itself in Rhue's sword too.
About the deam city that Rhue sometimes visits, maybe it contains all auras that Rhue has absorbed, or absorbed through the PS when he returns to Rhue. The PS's aura may be stronger because it also has the same ability as Rhue's..