Our closest private hospital is terrible on their maternity ward judging by what I've heard - I've not heard a single positive story about being treated well over there. I was so lucky to have a very small district hospital that was just like a private hospital anyway - choice of Dr and single rooms etc.
Mirabelle, I guess another thing is that even though PHI is very exxie, it costs the same for your public hospital stay as well, just that the public hospital tab gets picked up by the tax payer plus. I would be making use of it simply so you get some benefit from your PHI.
ETA - it's handled the exact same way as a private hospital stay - you give them your PHI details and they send the bill to them and depending on your level of cover you may have a gap payment etc - just as you would with a private hospital.

