When they first showed it on the previews, I thought it was going to be a PS90 or a FS2000, both of which would have been better platforms. Based on the show, it was an off-the-shelf bullpup stock kit. Might even be made by FNH.
In the show, the stock was a one-off. Joe even explained the process to Brooks--similar to one of those MakerBots where they plug in a 3D CAD drawing into a machine that spits out small layers plastic one on another until it makes the desired design, but a commercial machine.