Happy to elaborate without hopefully getting too boring for people!
Yes you are right, the broad conceptual foundation of the AMA methodology is sound and in fact the same as that for the MBS (at least originally). And CPI and AWE are independently developed, both by the ABS.
However, only one (CPI) is an index. Indeed, the ABS state in their own AWE publication (6302.0) that it should not be used as an index. It is highly volatile measure which, due to compositional changes over time and the presence of outliers (ie small numbers of very high wage earners resulting in an upwardly skewed sample), overstates wages growth. It has many uses, but indexation is not one of them. (An indication of just how skewed it is can be had by comparing the average annual salary, at around $82k, to the median,which is around $55k - that's just under a 50% difference!).
The AMA (as you point out) use AWE to determine ~70% of their annual indexation figure.
The CPI is an index, but it is not really an index of medical business costs, or in fact any business costs. It is a measure of consumer spending costs - retail goods and services like groceries, clothing and so on. So again, not really suited for the purpose to which the AMA puts it, although perhaps less statistically egregious, since there are few alternatives.
If it were some sort of academic research exercise, where you wanted a quick rule of thumb on changes in fees or medical costs, then I haven't got a problem at all with anyone using the measures outlined above - as long as they use appropriate attributions and caveats on the data. But we are talking about a system here that affects the health and lives of millions of people! Using such a theoretical construct, without the rigour of any focused empirical analysis (or even any attempt to conduct such analysis) tells me their focus is on maximising their claims for pay rises.
I am aware of the methodological differences between the Commonwealth and the AMA (as I alluded to in my original post) and Governments of all persuasions are not wholly innocent either. But whose figures are 'right'? I can definitely say the AMA certainly are not, and the Commonwealth are very more than likely not.
Both sides have preferred to play the politics rather than genuinely seek a consensus based on sound (and dare I say boring!) analysis. And guess who ends up the loser(s) ...?