Apologies to the DG for taking this off on a tangent....however....
Alan, Australian is fine (within reason!!!!) as long as you are from O/S or out of state:
Guests should be invited to play by a member of The Australian, unless they are from interstate or overseas, in which case they may be introduced by the General Manager. Manager introduced guests should be affiliated with a recognised golf club or association, and hold a current membership identification card or letter of introduction from that organisation.
You raise a good point about RSGC. I am reciprocal so I have always introduced guests through that affiliation, I guess. However, you correctly point out that you probably should not skip a round at NSWGC to play at RSGC ! That said, I think that, if they REAAAAAALLY wanted one, an international guest would get a game at RSGC with a well worded, polite, flexible letter to the GM.