The heart of the issue can be reduced to a handful of sentences, Glen. It's not that complex. And, with the greatest respect, continued voluminous correspondence with CASA or anyone else (other than a judge or tribunal member) will not change the heart of the issue.
CASA's position
CASA's current position is that, on its (recently conjured up) interpretation of Part 141 (and Part 142), APTA had not provided sufficient evidence to satisfy CASA that APTA had sufficient operational control over its members. CASA's position is that CASA was justified in demanding from APTA "a tabular legend, showing how and where the actions called up under each applicable provision of the civil aviation legislation germane to the conduct of operations under CASR Part 141 [and Part 142] are effectively addressed in the terms of the contractual agreement(s) [between APTA and its members]", before CASA would be satisfied.
(You should note that "CASA" here just means the subjective opinion of an individual, the identity of whom you can safely guess.)
APTA's position
APTA's position is that what APTA provided was sufficient to demontrate compliance with the legislation, noting that this assertion from 'CASA' is a fiction: "The operational and organisational arrangement contemplated by CASR 141 [and Part 142] are based on a conventional business model, under which all of the operational activities conducted by the authorisation holder are carried out, for and behalf of the authorisation holder by persons employed by, and in all respects as agents of, the authorisation holder.")
The practical problem
To get an authoritative statement of what Parts 141 and Part 142 actually require, APTA would have to spend years and hundreds of thousands, in a court or tribunal, battling master sophists wielding the 'safety' card. CASA will say that, absent evidence of how and where the actions called up under each applicable provision of the civil aviation legislation germane to the conduct of operations under CASR Part 141 [and Part 142] are effectively addressed in the terms of the contractual agreements between APTA and its members, those members could be out of control and creating high risks to the safety of air navigation.
If it makes you feel better to continue writing to CASA, what you should be asking for is specific authority for this proposition: "The operational and organisational arrangement contemplated by CASR 141 [and Part 142] are based on a conventional business model, under which all of the operational activities conducted by the authorisation holder are carried out, for and behalf of the authorisation holder by persons employed by, and in all respects as agents of, the authorisation holder." Ask CASA to cite a specific regulation, or a specific statement in an explanatory memorandum for Part 141 or 142, or the specific reasons of a judge or tribunal member who's considered the legislation, as authority for the proposition.
As I've said, the above is in my view regulation conjured in the mind of a complicator. The 'authority' for the proposition will, I reckon, boil down to 'the vibe' but expressed in enormously impressive but ultimately vacuous motherhood statements, assuming you don't receive the usual crickets chirping as a response. They don't care, because they don't have to.