I was a private pt but public hossy with DS, however in the country where Obs are extremely rare I just went through the m/w clinic and saw the same Ob (cos I was special lol) throughout. The hossy even paid our excess for us.

With DD though there was a risk I would need the public hossy so my Ob was just going to go there instead. We would have just claimed the hospital like you do at the private hospital.

Though it depends on your reason for going to the public hospital, they can't guarantee you a private room. When you book in there is a form that you tick whether you have private insurance and will be/will not be using it or if you are just a public pt.