As you seem to be able to have a rational discussion without switching to skygod mode, andrewr, I'd be interested in your perspective on this from the report:
ZPJ joined the Mildura Airport circuit on the crosswind leg for a left visual circuit to land on runway 09.
On the base leg of the circuit, the flight crew on board ZPJ heard their traffic collision alert system (TCAS) announce a traffic advisory (TA) aural alert (see TCAS limitations on approach). They glanced at their TCAS display to check the relative position of the traffic, which indicated it was to their right (position 1 in Figure 1). The flight crew looked out the right window of the flight deck and identified the traffic to their right and high against the skyline. The traffic appeared to them to be stationary in the windscreen relative to their own aircraft and with a high closure rate (from TCAS data the aircraft were 1.25 NM apart at the time of the TA alert).
I interpret that to mean that while ZPJ was on base, XGA was on final from a straight in approach. The fact that XGA appeared stationary to the crew suggests to me that the aircraft were on relative tracks that were highly likely to intersect at the same time in the same place. (I came to these conclusions while sloshing wine at the local aero club....)
You said:
Before XGA was instructed to go around I think things were OK, they were behind ZPJ in distance to the runway and more than 500' higher when ZPJ got the traffic alert. I assume the jet approach speed is greater than the GA8 so that should work. The XGA pilot was probably of the opinion that they had given way to the traffic in the circuit.
Is that based on any 'inside knowledge'?
If XGA appeared stationary in ZPJ's cockpit, ZPJ would have appeared stationary in XGA's cockpit, thus raising the question whether the pilot of XGA's opinion was correct (even assuming XGA saw ZPJ and had that opinion).
Why do you think they were "OK" in that circumstance?
(And Compylot and Bloggs: Clearly we operate in vastly different places, because I've never heard or had any 'insolent' interaction on any CTAF, or heard any benevolent skygod give 'mutally agreed instructions' or 'take control' in any CTAF. But maybe I just insolently leave my VHF switched off....
My only advice to you is when you switch to amateur ATC mode, ya better get it right. As I observed before, the good news for you is that the odds are vastly in favour of not having a collision, even before you open your mouth.)