Wasn't that case more dependant upon the fact that the fed can't appropriate and spend money for any reason it sees fit? That it has to come under a head of power? 116 was brushed over with minimal discussion (from memory, and still don't understand why tbh).
The way the government of the day got around that decision (basically "it's under a head of power because we say it is) is being challenged now in Williams 2: The Revenge. It seems pretty likely that the court will strike it down again, if my understanding is correct.
Yes, it's probably better to put it like this, there were two main arguments put forth by the plaintiff.
1) Freedom of Religion
The plaintiff argued that chaplaincy program infringed on freedom of religion by basically establishing religion and requiring a religious test for an office of the commonwealth which is prohibited by s 116 of the Australian Constitution.
The High Court rejected this argument.
2) Section 51 executive power.
The plaintiff also argued that the executive can not spend any money without firstly the approval from parliament, which also requires as a secondary corollary that any spending the government does comes within their normal legislative power. The parliament has never had unlimited power to spend, so therefore neither does the executive.
I don't have too much time to explain it right now, I'd be happy to give more info a bit later but basically it boils down to 'no taxation without representation' - Only our elected representatives (the parliament) has the power to levy taxes and spend money. This judgment is a logical extension of Pape v Commonwealth....which did delve into the history of the fact that the ENTIRE point of Parliament was to restrain the executive.
Edit: The issue in Pape was that the government couldn't just hand out oodles of money (this was the stimulus cash back program) because they didn't have the power to, the High Court agreed that normally the Federal Government DOESN'T have the power (which was a huge shock to the Federal Government) but they did have the power on this occasion as it was an economic emergency that required quick action.
In other news, the government won the battle in that case but badly lost the war.