Preamble
Yes. Payments to them are salary or wages and tax instalment deductions should be made. Refer to the definition at Section 221A of the Income Tax Assessment Act 1936 and Taxation Ruling IT 2129.
The fact that a person provides his/her own vehicle is not, on its own, a deciding factor. As an example, Real Estate sales people also provide their own car, own registration fees, expenses etc. and are subject to the PAYE provisions. Support for that treatment is found in the case of Peter F Burns Pty Ltd v Comr of Stamps (SA) 80 ATC 4220; (1980) 10 ATR 818.
Similarly, the degree of control or supervision, alone, can not be a deciding factor. Even though the instructor has special skills and cannot be continually supervised, the employer has 'lawful authority to command so far as there is scope for it' (Zuijs v. Wirth Brothers Pty Ltd (1955) 93 CLR 561).
As stated in Taxation Ruling IT 2677, the 'integration' test may also be relevant. 'This test is concerned with whether the individual is performing the relevant services as an individual carrying on business on his or her own account or whether the activities are part and parcel of another's business activity (Stevens v. Brodribb Sawmilling Company Pty Ltd (1986) 160 CLR 16 at 26).'
A person could be said to satisfy the integration test where : (a) the relationship is a continuing one; (b) the individual's activities are in effect restricted to providing service to one principal; and/or (c) the individual would not generally profit commercially from sound management in the performance of his tasks, i.e. the individual is so inextricably integrated in the business organisation of the principal that any benefit arising from the individual's work would flow to the principal.