CASA has treated the airlift component of skydiving as a private operation because CASA considers that the payment made by the parachutists is for the descent from the aircraft, not flight in the aircraft.
The only adjective I can think of is: Orwellian.
In the case of the parachutist passengers, CASA considers that the passengers are paying money only for what happens after they leave the aircraft.
But if a pilot flies passengers from - say - Adelaide to - say - Kangaroo Island for "free" for a holiday stay at accommodation owned and charged for by the pilot, CASA considers that the money paid by the passengers is part of an overall transaction for services that include the flight and therefore the flight is for a commercial purpose.
Passengers paying for enjoyment of experience X are apparently on board a private flight from A to B if X happens to be a parachute jump, but on board a commercial flight if X happens to be a holiday at Kangaroo Island. It's OK for a private pilot to be paid to carry the parachutists passengers to point B in the sky, by it's not OK for the same pilot to be paid to carry the same passengers to point B on the ground.
In the case of the parachutist passengers, apparently the money paid is attributable only to what happens after they exit the aircraft; not so for other passengers.
The safety basis for these distinctions are obvious: No fare paying passenger has ever died in parachute operations.
Orwellian.
Classification of operations rules have been broken forever, and it's obvious that CASA is incapable of fixing them.