I'm no aerobatic pilot and have not actively flown in years, but as I recall, part of inverted spin recovery (never did one - only upright spins) is full aft stick/up elevator ... also, rudder inputs are reversed when inverted ... left rudder to go right etc. Is that correct? If so, the cfi in the above example must have thought he was in an upright spin. I did a few upright spins in basic flight training (I think it was required back then), but none since. I have enough trouble visualizing the proper control inputs for inverted spin recovery while sitting here at my desk. I can appreciate how an inverted spin would be extremely disorienting to someone unaccustomed to them. It would be quite difficult to exit the back seat of a Decathlon while it was in an inverted spin. R.I.P. the cfi in the above example.
He had deliberately entered an inverted spin for the purpose of demonstrating it, so I strongly doubt he mistook upright for inverted.
Pro-spin and anti-spin inputs are not complicated, especially in a Decathlon, which is in most instances a very benign aircraft to spin. Roll inverted, push stick forward to stall, rudder in the direction you want to rotate. Recovery is rudder opposite rotation and neutral stick. Just like upright. It takes a lot of stick travel to stall or spin inverted; I have to grab the frame and do a crunch to get it far enough forward.
Disorientation is a huge problem in an aircraft like a Pitts, which rotates at 720 degrees per second. In a Decathlon, I never found it challenging. In an deliberate spin, you know what direction you made it rotate, so go the opposite direction to recover. The Decathlon is not like a Pitts, where you can accidentally transition to opposite rotation and orientation without knowing it.
I got my inverted spin training from Adam Cope, one of the most experienced Decathlon instructors in the country. He emphasized that 99% of the time, simply relaxing the pro-spin inputs causes instant recovery from an inverted spin. Since it is so awkward to get the stick far enough forward to stall, it is harder to hold an inverted spin than to break it.
There are some instances of an inverted spin where airflow over the rudder can be blanked by the wings, reducing control authority and ability to break the rotation. I don't know the nuances well, but power, ailerons, and CG can contribute to this condition. The response is to confirm power is fully off and stick is centered. Centered rudder should work, but rudder opposite direction of rotation works faster, or so I have been taught. If there is the possibility of confusion about direction of rotation, neutral rudder would be more reliable.
Back to the OT: the Pitts and its derivatives are far more challenging aircraft in the spin regime. They are also far more likely to accidentally spin than a Decathlon, which you would really have to work at. Several reputable instructors offer 5 or 10 hour advanced spin courses dedicated just to exploring the various modes of spinning a Pitts, such as flat spins, accelerated, and the effects of power on/off, aileron, etc.