Yes, I was a bit surprised when they claimed that changing the rectifier would require a complete power supply redesign. I've designed power supplies for many solid state amps myself. SS rectifiers have a lower voltage drop, so the rectified voltage would be higher. Consequently, the smoothing caps would have to accommodate the higher voltage.
I guess that higher smoothed DC voltage would be passed along to any regulation circuits, and potentially require more heat dissipation. (I have no idea what's in place in the SLP-05.) If there is no regulation, then the higher voltage would be passed along directly to the rest of the circuitry.
Therefore, I wouldn't feel comfortable trying a SS rectifier without the blessing of Cary.