The shift began in 1996 with Flinders converting from undergrad to grad. It did this, according to its own white papers (which used to be available on the Internet in the pre-security conscious days), because it was close to going bankrupt. The reason it was in such dire straits, as were many med schools at the time, is that the federal govt heavily subsidizes education here. It decided how many subsidized spots it would give, and it set the amount that it would pay the university for each student in any particular program, while preventing the unis from charging students more out-of-pocket.
Of course, such non-market pricing does not get the benefits of normal price signals, and it turns out that the federal govt was not only grossly underestimating the number of docs needed in Australia, going back to the early 1980s (according to a member of the AMA's advisory committee on the matter), but not allowing the unis to fully cover the training costs of the students. This was part of the impetus around this time that some of the sciences, most notably anatomy, was drastically cut back by pretty much every med school (cadavers are expensive as hell to procure and manage, despite the fact that it's illegal to sell them). I've heard the argument that this is also why schools switched to PBL, but people who you'd think would be most in the know claim that PBL is *more* expensive (and the change was made for education theory, aka ideological, reasons).
Since the federal govt wasn't at the time in the mood to radically increase domestic student funding, the way around this financial problem was for the school to ask for permission to allow int'l students to be charged much higher fees. The market told Flinders that it was N. Americans who'd be paying, and N. Americans are used to, and prepare for, grad entry. Ergo, Flinders became graduate. UQ switched the year after, and USyd one or two years later, both for financial reasons.
2007 was the first year that there were more grad programs in Australia than undergrad. Currently there are ~11 4yr programs, 7 5yr programs, and 4 6yr programs (a few med schools have more than one, and UWA is in the middle of phasing out its undergrad program). It's not a given that they'll all go grad, as a market-based system would benefit at least some to remain undergrad (UQ went somewhat back that way a number of years later by also accepting high school students who had top scores, promising them a spot in their grad program if they got a uni degree with reasonable marks). On the other hand, if the undergrad programs are forever financially inviable, they probably will all get fazed out eventually.
The latest trend is to offer the MD degree (first Melb, and then USyd and UQ, plus more I'm sure), which is actually a Master's degree here (vs. a professional doctorate in the US). Schools are doing this for two reasons. One, it's marketing of a degree title (particularly to N. Americans). However, note that Melb has always had chiefly Asian int'l students. The other reason is that there are fewer restrictions on course fees that unis can set for domestic students getting a masters. So again, the driving force is financial.