The article you linked to started:
NO doubt the Rudd government's big budget stimulus helped keep Australia out of recession last year. But mining was at least as important in producing the unexpectedly good performance.
I agree 100% with that conclusion.
Also, at odds to your point (1) above the same article says:
So the stimulus cash handouts and capital works look to have done most of the work by pumping up consumer and government spending. Treasury suggests budget stimulus added 2 percentage points to GDP growth last year.
It goes on to point out that this was insufficient in itself to explain the growth in the economy.
Clearly, demand stimulus by government hand-outs isn't a sustainable, long term model to grow an economy. BUT contra-cycle government spending can be an important tool to stimulate growth, especially through periods of uncertainty. (To make it clear this isn't a political point: Australia was able to do this because of large surplus budgets run in the period up to 2008/09 by the previous government. That was good policy during that period, and the stimulus was good policy during the crisis).
Note that in the US the stimulus package was radically smaller (compared to the size of the US economy) vs the Australian package. Additionally, it actually did reduce unemployment[1]. It is unfortunate that the US didn't follow that up, and instead made things worse via austerity measures.
[1] http://www.cbo.gov/publication/42715