The goose may be the ABC? The reporter or researchers may be guilty of not doing their homework. The compressor is not turned off. It is turned down, to a lower power/capacity mode of operation.
Energex has an explanation that may be easier to follow.
What actually happens with the air conditioner cooling depends on how each manufacturer implements their low power or economy modes. Inverter models can be turned down to run the compressor at a lower pump load. The reduced capacity as a heat pump reduces the available cooling capacity and electrical load.
For an already cooled room over 30minutes this is unlikely to be noticeable. If the air con has just been turned on the air blowing out will be still be cooled, however it will be missing the chill of full power. Maximum cooling comes back once the peak demand event is past.
We had a ‘peak smart meter’, more sensibly described as a remotely controlled demand load response switch installed with our new split in Brisbane 3 yrs ago.
Per the table in the Energex link above, reducing the air con power is an uncommon event.
Fitting the device has been a great deal, with no noticeable loss of cooling or increased costs on the bill.
Previously we have used the controlled supply tariff 33 for our air conditioning and pools, in Central Qld and FNQ. Every little bit helps. It also helps the grid shed load as needed. But you do loose all connected cooling up to two times daily. Alright in a well shaded and insulated house with ceiling fans all round.