Yes they can ,
because when you make a transaction from a Debit Card anywhere but the Australian EFTPOS saving network (Pos terminals and Savings/check button)
you are using the Visa / Mastercard global network and the Visa / Mastercard sets the fees for transactions through that network
- Anywhere online or direct debit where you enter the Card Number on the front
- Tap at register: if the machine doesnt support EFTPOS
- overseas
Its irrelevant if you have money in the bank account all that matters is the network that handles the transaction and the banks will at their discretion pass / inflate those fees onto us
The Visa / Mastercard logo on the front of our cards are a feature not a bug, a means to increase cards compatibility around the world and online, but the trade off is Visa / Mastercard call the shots