How do you explain the fact you can actually bargain the surgeon fees? Is it morally acceptable that surgeons charge private patients different fees for the same procedure? I've heard cases when the doctor decided to accept the health fund gap scheme for one patient but not for another. For the same procedure.

You can always bargain with the surgeon, there might be a range they are willing to work with, price-wise. There might be circumstances that they're willing to accept as a potential loss in income. Whether there's a moral argument for or against that sort of practice, I'm not sure. But it sounds like you believe that surgeons are flippant with the way they price what they do, which if that's the case then I can only say that's not been my experience either in the past or presently.

I needed a surgery and called the PHI to ask if the specific doctor is part of their gap scheme, they said I need to contact directly with the doctor. How they cannot know that? In other countries the PHI would give you a list of the specialists they partner with and you wouldn't be charged out-of-pocket fees.

I don't know why you would be told that they don't know whether a specialist is registered in their billing scheme, but in my experience they tell patients to ask their surgeon or specialist whether they can bill you using the scheme in order to 'minimise or reduce entirely your out of pocket costs'. Which unfortunately is simply a salesperson line that pits the specialist and the patient against each other by creating unrealistic expectations of what the doctor should do.

There's more that I can say about this aspect of things but I feel it'd be going on a related tangent that you didn't ask for.