Hi @MaryAnnie
Some surgeons do treat you as a private patient in a public hospital. The hospital uses your private health insurance details to fund the hospital but they don't charge you the health insurance excess. The only issue is that if it is a teaching hospital the hospital can override the surgeon and, whilst he/she is in the room supervising, the surgery could be done by a student. Check with your surgeon how he/she handles this aspect. The hospital may pick up the excess costs such as the anesthetist and bloods - again, check so you have no surprises.
Hope this helps. Summer :)