Public sevants are part of government.
Nope, public servants are part of the Australian Public Service.
The APS serves the government, but is not part of the government.
Specifically, according the Public Service Act of 1999 it is an "apolitical public service that is efficient and effective in serving the Government, the Parliament and the Australian public".
Our government is comprised of three groups:
1. The Executive - basically the boss, which in 2018 is still unaccountably the governor-general.
2. The Legislative - elected officials in the lower and upper house (we choose these guys and gals), who are given their power at the whim of the boss
3. The Judicial - the high court who connects the legislation with the proles like you and me
It is the job of our elected officials to make sure the customers (us) are getting value for money from the contractors (the Public Service). The APS is accountable to the government (ostensibly), and the government is accountable to us (ostensibly).
In reality, we have very little control over our government, because most of us don't understand how it works well enough to know which elected official is doing a good job.
And the government has very little control over the public service, because the government comes and goes each election, whereas the public service is unchanging.