No spin. Apparently pilot induced high altitude upset
Indeed the incident commenced with a pilot induced "upset", but that was at cruising altitude. So far as the spin is concerned, I can only quote the Captain, speaking just after landing.
I know the reports don't mention that, but that's what he said, and it's entirely plausible that the aircraft could have eventually entered a spin after the other gyrations it went through.
The interesting thing was that a team of engineers from Boeing and QANTAS spent many days inspecting the structure minutely, and found almost no structural damage from pulling well over 4G and -.63 G. Do they still build them like that?
The CC said that a baby flew almost the whole length of the economy cabin during the negative G period, and landed unharmed in an empty seat.