Wrong. Mostly, someone of age pension age they can, if eligible (under income and assets tests and Australian Working Life Residence rules etc), have their pension paid overseas
https://www.servicesaustralia.gov.au/when-you-leave-australia-if-you-get-age-pension?context=22526
https://www.servicesaustralia.gov.au/payment-schedule-and-rates-for-people-outside-australia?context=22526