Here is the relevant text from the Qantas website re Qantas Club members:

Dedicated check-in
To help avoid queues, members may use The Qantas Club priority check-in areas available at most airports. If there is no dedicated Qantas Club check-in, you may check in at the Business Class counter prior to any Qantas flight, regardless of your fare class. You must be travelling on a Qantas operated service with a Qantas flight number. If only carrying hand luggage, and travelling on a Qantas* or Jetstar marketed and operated flight, you can also check in at any major domestic Australian or New Zealand Qantas Club lounge

It really is an issue Qantas should sort out (assuming they know about it). If they know of it but don't rectify it then they are being very irresponsible. I have a Singapore trip planned late this year and will certainly, in light of Austman's issue, be clarifying the situation prior to travel.

And I'll have to confess, despite having lived a number of years in Singapore (in my much much younger days) I do not know who or what SATS is.

Regards
Chris