Greg: Could it be the 'missing' "only" in the side wire spec. The 'push' "only" is definitive and straightforward.
As I did primarily comm work, stranded was common. Termination was 85% on spec grade devices with the screwplate side wire. The other 15% technique was the small piece of insulation on the tip of the conductors. Never used a sta-kon.
I was just looking at the cheap side wire device and the word "stranded" is conspicuously absent. I read the "only" to preclude 12ga in a back stab. I am not sure if they just left out stranded or they are saying it is not appropriate for that device. (110.3)
I see on the spec grade with the clamping terminal they do say stranded.
There was a movement a few cycles ago to eliminate the push-in terminals on receptacles entirely, but a lot of residential guys liked them. The compromise was to allow them to continue to be used but limit them to 14AWG and 15-Amp circuits.