here in Australia the Red Cross and Salvation armies had permission to use army unit and formation signs on the vehicles they used.
I can only assume that the vehicles, while probably purchased outside of Army purchases, were painted to match the units they were with.
AWM pics of salvation army personnel and their vehicles show them in military uniforms as well.
I have recently bought a read only CD of Australian Formation Signs and Vehicle Marking of the Australian Army 1917 to 1983, by Steve Taubert,
Comtrain Enterprises
20 Friarbird Drive
Narangba
Qld 4504
which contains a wealth of information on these type of markings for the Australian Army.
I also noticed in the above photo of the chev ambulances that they are fitted with dual rear wheel hubs and yet are only on a single rear tyre.