The main confusion seems to come from the assumption that if it can be performed under a PPL, an AOC must not be required.
I don't see why that has to be true. AOC requirements and private operations are defined in different places, using different criteria. I don't see the issue with an overlap (it seems essential if you look at the definitions). If you can say CPL is not required but AOC is required then it is not too hard to interpret.
Of course, there is nothing stopping a requirement that operations be performed by a CPL being written into the AOC.
I have a faint suspicion that the problem with this interpretation is that some in CASA have used the "private operations" definition to rule that an AOC is not required instead of CAR 206...