4dogs. Airspace management can be delegated by an Arbiter to a third party (I work lots of other sovereign territory airspace where I am {not Australia}). These delegations will be spelled out in Letters of Agreement, which are lodged with ICAO. Any disputes etc. will be mediated by ICAO. However, an Arbiter can, and does, require the airspace be managed in certain ways i.e. impose their own rules on the delegate.
In short, I am not sure what the LoA says in this case, but Australia is well within it's rights to require the airspace be operated in a certain way. I think this is what Heffernan is getting at; why hasn't AsA taken action to ensure the airspace be operated to standards that Australia sees as fitting, regardless of who is doing the operating?