OK - You do have to get a specific referral for the NT scan - at least in Victoria. The 12w checkup at the hossy is just a dating scan, where they check the CRL and ensure that your dates all tie up OK. At our hossy they really dont have the correct equipment in that part of the hospital for this scan. I'm not sure whether this is what you mean or not...... Maybe I'm on the wrong wavelength from your post? I apologise if I am.
Most drs dont make a big deal of the scan unless you are more likely tobe at risk. Soif you have had previous problems or you are older (normally 35+). This is another reason why its not covered under Medicare.

If you want to get a check done, can I suggest the Triple screen test, where at about 15w they takea blood sample and give you a risk of abnormalities (I believe downs, and trisomy) based on your age and your blood. This is fully covered by Medicare. No out of pocket costs.
From here - if you have an elevated risk, they will refer you for an amnio, which would be covered under Medicare I believe - or at least some portion.

I get that you are pi$$ed - this happened to me too with my first pregnancy, and I was a little miffed, but then I got the blood test back and I had next to no risk, so it may have been a waste of money.
But the important thing to ask yourself is - will the blood test give you the answers you need, and what would you have done if the scan had shown something.
I know its not much consolation, and you must be fuming inside, but maybe a call to the dr tomorrow will help sort things out.