It is common for Medicare staff to get this wrong.
I simply sent a email to Medicare saying exactly why my partner would be eligible and got them to confirm that it was correct (took 3 emails). I did say it was required because the staff are not familiar with immigration. This was their second reply.
Thank you for contacting the Australian Government Department of Human Services (DHS).
A person is eligible for Medicare if they have both:
• a current visa authorising their stay in Australia. - visitor visa in your case.
• lodged an application for permanent resident visa (excludes an application for a parent visa) with the Department of Immigration and Border Protection and have permission to work in Australia or can prove relationship to an Australian Citizen or permanent resident visa holder. - other requirements may also apply.
To enrol in Medicare, you are required to present your passport (including your permanent residency stamp) and/or a visa grant letter or email from the Department of Immigration and Border Protection (DIBP) and one other form of identification at a Human Services service centre. You will need to complete an enrolment application. For your convenience I have attached an Enrolment application form.