As a CAA TA, let me clear this up.
Disney gives CAA/AAA a certain number of rooms/packages at a discounted rate. Sometimes, we sell these all and there is no discount to book with CAA. This applies at really peak times, most of the time, the discount is available with CAA as long as something is available.
You can book either the package, or the room only, at a discount. You might be able to do this with Disney, but I have no idea...
CAA is not able to change the rates given by Disney. Once a rate is given, it can't be discounted, we have no flexibility there. However, we usually have the lowest rates compared to booking directly through Disney.