Yes but no, at least in the first instance, and then it can be complicated. From the (previous) FOS website, cleverly presented in a pdf Google found. I could not find a link on the current AFCA site and it is possible but unlikely anything changed since FOS was rolled into AFCA, so pardon the extracted paste-in. Bolded italics added. @Gregr , I note your methodology is best practice
Fact Sheet
Mistaken internet payments
Internet banking
Internet banking is an easy way to electronically transfer money from one account to another. It is important to get the BSB and account number right, because banking systems only use the account number when processing the payment. The account name is not used to transfer the payment.
It is important to check (and double check) the account number when entering it in your internet banking system for the first time. If you are making a big payment, we recommend you transfer a small amount first and check that the payment has been received. If you have sent money to the person before and they are in your preferred list, make sure you choose the right person when making the payment.
What is a mistaken internet payment?
If you do enter the wrong account or BSB number the payment will be made to the wrong account (unintended recipient). This is known as a mistaken internet payment.
The ePayments Code sets out a process that will help consumers get your money back if it has gone to the wrong account. The ePayments Code is administered by the Australian Securities and Investments Commission (ASIC)i. The Code does not apply to small businesses who make internet banking transactions.
What if I transfer money to the wrong account?
If you have made a mistaken internet payment, you need to contact your bank or credit union immediately. Your bank or credit union will then contact the unintended recipient’s bank to try and get the money back.
If the money is still in the other person’s bank account and it is a genuine mistake (because the account name and number do not match), then the process for recovering the money depends on how quickly you have reported the mistake to your bank. If you report the mistake:
Within 10 business days : the funds will be returned to you.
Between 10 business days and 7 months : the recipient’s bank will freeze the funds.
The recipient will then have 10 business days to show they are entitled to the funds. If they do not, the funds will be returned to you.
After 7 months : the funds will only be returned if the other person agrees.
If the money is not in the other person’s account when the receiving bank is notified, then the receiving bank must make a reasonable attempt to get the money back. For example, by negotiating with the unintended recipient to repay the funds.
If your bank or credit union does not help you to fix the mistaken internet payment, you can lodge a dispute with the Financial Ombudsman Service Australiaii.
What if money is incorrectly transferred into my account?
If money is incorrectly transferred into your account, you should notify your bank. Your bank will then try to return the money to the sender.
You should not spend or withdraw the money transferred into your account by mistake because it is not legally yours and you have to pay it back.
and the pdf advisory goes on to comment on Bpay and unauthorised transfers.