I think he has a tacit control over the show at best. I have no doubt there are some basic parameters that are set in place. And, there is at least a meager effort to screen callers. Wes Durham was formative for Brandon as he passed the torch not only on game broadcasts but on working with Paul in general. So there is a culture that is set in place, and Paul is a part of shaping that culture.
I believe to Skeptic's general point--there's not a coach's show in America (probably) where the basic idea isn't to make it as favorable and fan-friendly as possible. Above all, the school and team are supposed to come out (on balance) looking good. Of course. What idiots wouldn't see to it that this was the case? No major D-1 football call-in show is set up to be a wide open media scrum, nor a place where "enemies" (you like what I did there?) get free shots with their agenda.
However, if you listen on a regular basis and particularly if you are in the room on a regular basis-- you know that it's not all softballs teed up for CPJ to swing at. Troll calls slip through, a few honest/real questions get asked every week. Things that challenge him to respond to will be there every week. And, especially in Brandon's first season his learning-curve on GT football caused him to bring some questions that Paul didn't always care for. You'll see the tension in the room when he gets a question that he doesn't care for. Then, it's up to him as to how he responds. Some of them he responds to with more vulnerability, some with less patience. Sometimes he comes off a winner on those, sometimes he can make himself look a little less good.
But, it's not an hour that is as carefully controlled as some might think.