On the ACCC site, there doesn't seem to be anything about fuel cards being treated the same as credit cards: Excessive payment surcharge ban
So it would seem that as long as the retailers charge a 'reasonable' rate to recoup the cost of servicing the transaction, there is no issue. AmEx and Diners merchants charges are higher than the three cards listed at the top of the photo. Given that all the lower volume cards are charged at the same rate, it is probably not excessive.
So to my mind, whether a fuel card is treated the same as a credit card or not, it's probably reasonable to charge the same as AmEx and Diners.
The advantages of a fuel card are the
1. (occasssional) discounting associated with the card,
2. tracking of all work related monthly fuel usage and associated and expenses in one place, and
3. the advantage it provides for claiming GST and other business taxes.