The quality of SSAT is bound to vary, just like other aspects of training. Instructors (like every other profession) come in all varieties from excellent to less than excellent, even the good ones aren't good at everything on every trip of every day. Training aeroplane types are not all equally good at demonstrating the different aspects of flight, I seem to recall that part of the reason that spinning was removed was because not all "modern" training aircraft were cleared for deliberate spins.
Although I don't do very much basic PPL training (mostly aeros, multi, IMC or tailwheel) I always try to encourage PPL studes to do at least one spin trip. All aircraft are capable of spinning if encouraged in the right way, IMHO the chances of a PPL recovering by themselves if they have never seen a spin before are nil - their only hope is if the acft spirals out of it.
This is not to say that spinning is dangerous, simply that it can be a little overwhelming the first time you experience it - after a few they become fun.
So my vote is firmly in the "it should be part of the syllabus" lobby, if some FIs are uncomfortable with this they should receive additional training. I also think that some aeros experience should be mandatory for all FIs and that the sky should always be blue and that Melinda Messenger and Angelina Jolie should take a personal interest in slightly older FIs and that..... but the realities of life will prevent many of these wishes coming true.
So, if you're at all worried about stalling or spinning the advice is to find an experienced sympathetic instructor with a suitable aircraft (Tomahawk, Bulldog, T67, Citabria, or something more exotic) and treat yourself to a session of spinning. It will make you a safer and more competent pilot. If you fly something that will spin inverted or flat (Yak comes to mind) then find an aeros instructor and go and explore this part of the envelope in safety before it sneaks out from a dark corner when you're not expecting it.
Here endeth the sermon.