So, based upon game mechanics alone, the types of aircraft that are allowed at airports depends on the relative size of the airport. You'll see on the airport information screen that ANU is in the "Small (2)" size class. This means that only small, medium and large class planes can fly to/from it, therefore excluding the extra large class. As a side note, a (1) size airport will also not support Large class aircraft.
Therefore, the proper way to challenge the ability to fly a 777 to/from here is to argue that it should be classified as at least a Medium (3) class airport, as historically, I have not seen the administration make one-off adjustments to this particular rule.