Rob Ryan has been known to be very outspoken, just like his brother Rex. The Saints are trying to limit his exposure with the media by putting in his contract that he can only talk when he has permission.
As you can see from the Tweet above that goes against some of the NFL media rules. With that being saidm the Saints can simply say they gave him permission for his weekly appearance, but when it comes to outside stuff they are going to put a muzzle on him.
They must be paying him very well to get him to agree to something like this.