I don't think this is true everywhere. Queensland has the QAS[1], operated and funded by the state government. There are no (direct) fees.
There's no cost for ambulance treatment and transport for Queensland residents. This includes treatment and transport that takes place in other parts of Australia.
If you don’t live in Queensland, you’ll be charged for ambulance treatment and transport. If you have ambulance cover in another state it may cover the cost for you.