I have a few friends with them, two of which are police. You are not attaching the stock to the frame of the handgun... you are not altering the frame to accept the stock in any way. That frame is registered as a handgun, NOT a rifle. Like their website states, it is just an accessory. Think of a buying a .22 conversion kit for a 1911 and such. You are attaching a slide that has a longer barrel and stock, but the FRAME (IE the registered part) is still a pistol frame and registered as one. I purchased one used off a state trooper friend, then traded it back into a shop. I have watched them take 1911's and Glocks and field strip them to install the upper before a carbine match. I don't see the issue. Like others have stated... they have been around forever.
Selling converted Saiga 12 + Mags for $1000 PM for details.