They are pressuring the airport to remove their landing rights if rumors are correct.
I'm almost certain that would be, at best, highly inappropriate, and at worst, near illegal. I can see state govt removing BI from carrier lists for staff travel but I doubt that would impact even one ticket per year and would be a symbolic gesture. But govt pressuring a private entity to revoke something that is the remit of the Feds... nup, I call rubbish on that rumour. Not least of all because it's not even the airport's decision to make.
As this woild come under the "external affairs powers" a state government "COULD" ban a foregin aircraft from the state but would be subject to reversal by the feds [not sure but I think specific legation would be required], It would NOT come under the free trade power as bruni is not a state.
I'm not sure I understand the latter part re free trade power. Brunei is a sovereign state and its government is signatory to any number of international aviation agreements that are administered in Australia by the Commonwealth, not individual states.
And as tullamarine points out, airports are on commonwealth land - they're not even subject to state government EPAs, though in practice as good corporate citizens they work with them, e.g. noise, water runoff, etc.
I'm also pretty certain that were an airport to revoke the ability of a carrier to land, whereby that carrier has complied with all contracted requirements, you'd have a lot of very nervous airlines from less than terrific liberal democracies that would question services and growth. So, not great for business. Also, legal recourse by BI would likely be successful.
And a private company pressured by a state government, I mean, come on, we're not that kind of state. Government doesn't work that way, despite what we all think as some winky winky backroom dealings.
To be honest, BI has such terrifically low fares year round out of MEL that I'm surprised they keep the route alive. Does anyone have an idea of loads? Oh wait... I'll check the BITRE numbers.