This is incorrect, for UK residents , due to reciprocal agreement with Oz which provides access to medicare and basic healthcare provision. all that is required to satisfy the visa requirements is proof of medicare entitlement. while desirable to have private healthcare (especially ambulance cover) there is no need to have it to satisfy the visa.
your quote is mis leading as it is written for all nationalities - most of which do not have the benefit of a reciprocal agreement as UK residents do. those who are emigrating on a budget need to know their options / risks. private healthcare can be expensive for temp working visitors so please be aware it is desirable but not an essential if you are UK resident and apply for medicare.