Some of the provisions of the Civil Aviation Act:
4 Application to state aircraft
Except where the expression state aircraft is used, references in Part III or IIIB or section 98 to aircraft or air navigation do not include references to state aircraft or air navigation by state aircraft.
state aircraft means:
(a) aircraft of any part of the Defence Force (including any aircraft that is commanded by a member of that Force in the course of duties as such a member); and
(b) aircraft used in the military, customs or police services of a foreign country.
Australian aircraft means:
(a) aircraft registered in Australia; and
(b) aircraft in Australian territory, other than foreign registered aircraft and state aircraft.
So it seems that if an aircraft is neither ‘of any part of’ the ADF (in this example) nor ‘commanded by a member of’ the ADF ‘in the course of duties’ as a member of the ADF, it’s not a ‘state aircraft’.
The organisation that does basic flying training for the ADF at Tamworth in aircraft with 'VH' on the tail presumably deals with the issue you raised, somehow. Sometimes those aircraft have an ADF member as PIC, in his/her capacity as an ADF member (= state aircraft) and sometimes have a civvy (contracted instructor) as PIC (= not a state aircraft).