People make legal statements swearing to respond to these situations no matter what. It's not an argument for universal health care. They know the risk of getting in the business, or at least they should.
If you were to read between the lines, you would find that it is. Under a universal health care system, doctors would never be faced with these dilemmas. Shall I put it in premise and conclusion form for you?
I now get what you're saying, and it's a good argument. Plenty of people come into hospitals, and they do not know their financial records. They just do it with or without the person's proper consent, but I just can't imagine charging someone for something like that, when they do not give permission for it to happen.
Of course, they are already presuming by operating on him.
Even if they were in full knowledge that the patient would be unable to pay, they should feel obligated to provide minimal care necessary to prevent his death. Especially as doctors, they can't just sit there and watch the patient die just because it's not a revenue-generating procedure.