What a load of crap. Australia wasn't even in the Empire in WW2. How could Churchill sacrifice it?
By World War II, Australia was an equal part of the empire (that is, legally speaking, Australia was just an important as the United Kingdom) but it was still part of the Empire. A loose parallel might be drawn by saying that legally Wyoming is as important as New York State, of course - there's a lot of difference between being legally as important and as powerful and significant).
Legally Australia was entitled to have its own defence policy. However the Dominions (Australia, Canada, New Zealand, and South Africa) had voluntarily chosen to remain part of an imperial defence system. We were free not to - but we'd decided that we would be involved.
Basically the Empire's defences were considered to be all of one piece, not separate national forces.
Britain was committed to defending Australia from attacks in South East Asia. In return Australia was committed to working to defend British interests anywhere in the world.
What wasn't considered was what would happen if there was a situation where Britain was under threat - and Australia was under threat at the same time.
When World War II started, Australia responded under its obligations to fight in support of Britain - this was done in Britain, and in Africa mostly.
When the war in the Pacific started, Britain was so intent on home defence, it couldn't meet its commitments to defend Australia.
But we were part of the empire and our forces were part of Imperial forces.