My daughter had dental surgery recently - was to be in the town I live in (no private hospital for a thousand miles in any direction) so it would have all been covered. We chose to have it done in Adelaide, for timing reasons and we happened to be there. Everything was covered except the Anaeth - he was a couple hundred out of pocket - surgeon, hospital, etc all covered by medicare and private health, who had an agreement with the hospital.
What wasn't covered were the CAT scans that "Dr Jones & Partners" (in crime?) did. more than all the rest put together - because the surgery was dental, Medicare didn't cover it and neither did private health (even on top cover).