I'm not sure how to work these threads properly, but I've read what George Lombard has said.
My sister and I had to deal with exactly this question recently on behalf of my mother, so I hope this will help.
Mum was in Oz, on a touruist-visa with 8503 in it. My sister in Perth took Mum's pbuttport to a DIMIA office (not the POPC) and asked there. She was told categorically that it would NOT be possible for Mum to make a valid application for a Contributory Parent visa if Mum herself was on Australian soil at the time.
Later, I read Booklet 3, all the main web-pages as well, and also - in the main web-pages - there is a specific link to "Visa Conditions." Reading the whole lot, I came to the conclusion that what the DIMIA official told my sister is right.
With Mum, we decided that the simplest thing was for her to come back to the UK when her tourist-visa expired, and to sort ourselves out from there. The risk with trying to lodge an application for a CP visa from within Australia is that if the "application is not valid", DIMIA will reject it out of hand, but they will NOT refund the application fee, which is currently $1305 AUSD.
What your parents could do, however, would be to lodge an application for a CP visa from outside Australia, and then return to Oz on another tourist-visa during the processing period.
That is what we did with Mum. I e-mailed the POPC and explained what we wanted to do, and asked for advice. They were brilliant. They said we could get the medical done in advance of making the application, since the medical is valid for a year. We could then apply for the CP visa and apply for another tourist visa at the same time. They suggested (since Mum is over 70 and therefore needs a medical certficate even for a tourist-visa) that we should ask the Panel Doctor to complete the tourist- medical at the same time as doing the main medical form.
For a start, that saved bunging Mum's NHS GP a further å£60, because the Panel Doctor refused to accept extra for doing the tourist-medical as well, plus saved Mum having to see two different doctors etc.
I sent off both applications simultaneously, one to the POPC and the other to the High Commission in London, and the tourist-visa arrived 10 days later. I was therefore able to get Mum back out to Australia in time for Christmas with her only grandchildren, who are out there. If DIMIA decide to grant the CP visa, Mum MUST leave Australia before DIMIA are ready to grant it.
So for what it is worth, we have not found that 8503 really imposed any great hbuttle. I think it is far more important to make SURE that your parents would be OK on the Balance of Family test and also OK on the health- criteria. Both are applied very stringently, and both are harder to interpret accurately than they appear to be at first sight.
I hope this helps.