For a period of time the holder of a PPL was required to be trained and endorsed for various types of airspace (I cannot recall exactly, but certainly 1990s at least early 2000s when I was doing PPL flight tests) Under the ICAO guidelines a PPL holder can fly in controlled airspace, so CASA dropped the airspace limitations to harmonise with ICAO. Under the transitional arrangements from CAR 5 to CASR Part 61 all PPL holders were considered to be trained and competent to operate in controlled airspace. As stated earlier, Part 61 requires training in all types of airspace (may be simulated if not practical to operate in it due to remoteness of training location).