Joel- I am sure you are right about Embry-Riddle's current practice regarding spin training. I am pretty sure Bob's instructor came from Riddle Field in Clewiston, FL, where Embry and Riddle operated No 5 British Flying Training School for the RAF. They flew Stearmans and AT6s supplied by the USAAF, the instructors were American civilians. I know this because my dad got his wings there in 1942. The maneuver described is a "falling leaf" which he taught to me in the late 1960's.
I use the falling leaf as part of my spin syllabus geared to CFI candidates but would strongly recommend that every pilot get some spin training beyond the basic FAA private pilot requirements. That doesn't mean you should go out and practice spins regularly in the family Cherokee, but awareness of situations that may result in a stall-spin accident may save your life some day.
Let me share a real-world example. Several years ago, I was giving primary instruction to a high-school student in her father's C150. She had about 5 hours in, progressing well, we had done some stalls and she was pretty comfortable in the air. She did have a tendency to be a little lazy with her feet, however. One hot day we were practicing slow flight, in the 150 with full flaps you need full power to maintain altitude. Lot of P-factor. I asked for a 90 degree turn to the left, she rolled into about a 20 degree bank with a healthy touch of left rudder. That little 150 IMMEDIATELY snapped into a fully developed spin to the left. I looked over and she had the wheel fully back with full right aileron- instinctive response, nose down, rotating left. We are in an accelerated spin with full flaps, full power, and inputs to flatten the spin. I took control, closed the throttle, retracted the flaps, and recovered immediately.
I asked her what had just happened, she correctly surmised we had been spinning. At that point, we changed plans, climbed up to 5000', and spent 30 or so minutes learning entry and recovery from spins. At the end of the flight, she was comfortable with the inputs for recovery, and a lot more aware of the need for proper coordination. If this had happened while she was out flying solo, I am pretty darned sure I would have been explaining to her dad and the FAA why my student spun herself into the ground.
She has subsequently had some formal aerobatic training with me after getting her private and I feel is a much more competent and confident pilot because of it.
I am not suggesting that anybody should go out and try to duplicate this event. This is not something that I would ever do intentionally, but it was certainly a dramatic reminder that a stall-spin accident can sneak up on you with little warning. I have spun 150's many times but have NEVER seen a spin that was as startling as that one.
To address your concern about teaching something not required and have the FAA come down on you if your student has an accident, that is frankly ridiculous. You should be far more concerned about your student having a stall-spin accident turning final and having to explain why you HADN'T taught them adequately how to avoid it. I teach people how to loop and roll my Decathlon, I don't lose sleep over worrying about whether they are going to go out and do it in a 172. Aerobatics are for aerobatic aircraft and that is stressed as part of the training. However, I have had one former student contact me after a wake-turbulence encounter causing him to roll nearly inverted, and was happy to report he simply rolled back upright.
I don't know the answer to the stall-spin accident problem, it continues to happen with alarming regularity despite efforts to the contrary in training requirements. I do believe the "Spin Training" which many CFIs receive is inadequate, and too many instructors are simply afraid of flying anywhere near the edges of the performance envelope of their aircraft. This is communicated to their students, we don't get better pilots as an end result.