I'm not convinced that CAR 206 defines private operations at all.
CAR 206 defines Commercial Purposes "For the purposes of subsection 27(9) of the Act". Subsection 27(9) deals with the purposes for which an AOC is required - not the requirement for a commercial license.
CAR 5.78 defines what a Private Pilot License allows you to do "to fly an aeroplane as pilot in command, or as co-pilot, while the aeroplane is engaged in a private operation" with the note:
"Paragraph (d) of subregulation 2(7) sets out the operations that are classed as private operations."
It appears to me that paragraph (d) of CAR subregulation 2(7) defines private operations, not CAR 206.
The assumption that private operations are operations that are not commercial seems incorrect. CAR 206 lists:
(ii) aerial spotting;
(iii) agricultural operations;
(iv) aerial photography;
as commercial operations.
Subregulation 2(7) paragraph (d) lists
(ii) aerial spotting where no remuneration is received by the pilot or the owner of the aircraft or by any person or organisation on whose behalf the spotting is conducted;
(iii) agricultural operations on land owned and occupied by the owner of the aircraft;
(iv) aerial photography where no remuneration is received by the pilot or the owner of the aircraft or by any person or organisation on whose behalf the photography is conducted;
as private operations.
This seems to say that e.g. agricultural operations on land owned and occupied by the owner of the aircraft are commercial operations that require an AOC, but can be performed with a private pilots license. It seems clear that an operation can be both commercial and private.
Subregulation 2(7) paragraph (d) also lists
(i) the personal transportation of the owner of the aircraft;
as a private operation, which seems to mean that transportation of the owner of the aircraft is definitely a private operation. There doesn't seem to be any restriction on what the owner does at the destination, except that CAR 206 says that carriage of goods property of the pilot, the owner or the hirer of the aircraft for the purposes of trade requires an AOC.
I don't know the definition of "goods for the purposes of trade", but it seems that it must be goods for sale, not just tools of trade. If CAR 206 includes tools of trade it would seem, for example, that a commercial pilot was forbidden from carrying a pilot's tools of trade without an AOC. Or if you assume a pilot is somehow exempt, what about a salesman carrying a mobile phone on a flying holiday? How far do you extend tools of trade? Do I need an AOC to check work email at my destination, if I carried my smartphone with me?
Whether this is how CASA interprets these regulations I don't know, but that is how I read them. Ultimately, it is CASA's interpretation that matters, until you are prepared to pay a lawyer to go to court and challenge them.