I see CM Punk is still a white belt. He sure has made a lot of strides since the last time it was publicized that Punk was training with him in jiu jitsu a long time ago. . .still being a white belt and all.
I question whether he actually trains or if this is just a publicity stunt. How can he possibly still be a white belt if he's really training?
Punk most likely doesn't have time to train the normal amount seeing how he's on the road, so it's not that strange. Even if you train 2-3 times per week it will generally take you about two years to reach blue belt level. While Gracie Academy says that Punk trains regularly with Rener I think he'd have to strain his schedule to be able to train once per week, so it's possible that Punk stays a white belt for several years.
In BJJ you generally don't advance as fast in the degrees as you do in arts like karate etc (the traditional Japanese arts usually have a tighter structure to that as well). Of course things differ even between styles within the same martial art, as well as with different teachers, but the original norm in BJJ is quite slow advancement (they also have fewer degrees than most traditional belt systems) and the Gracies are as original as you get.
To put it in some MMA context, Anderson Silva captured the Shooto title and fought in PRIDE while he was a blue belt.
So I don't think it's just a publicity stunt, although that aspect is of course always present since the sport and the gym of course gets more attention through it.
Edit: I was late and didn't see Thanos' comment. I didn't know Punk had said that.