Most of the NOs in Anniversary were simply dependent on a territory (or territories) being held by one side, so UK often gets a NO for the US controlling the Carolines in the Pacific, or the US getting a NO for the UK controlling France, or Russia getting a NO for the UK controlling Norway, Finland, and Poland. It’s basically the same thing; ANZAC was closely connected to the UK still, having been colonies/territories in the British Commonwealth/Empire up until just before WW2, so a good deal of British economics was affected by the status of Australia and New Zealand, just as it was with Canada (which is recognized in the game as an independent nation with their own roundel, but controlled overall by the UK player).
You don’t have to have the same person control ANZAC and UK for the NO to make sense, just like you don’t have to have the same player control the US and UK in Anniversary.