Yes, it is quite possible that they left out some information, and I don't know them well enough to feel that I can probe more deeply.
They did mention, although I don't know if the hospital said this or if it was their own speculation, that the consultants don't want private payers because of the hassle of collecting the money and the risk that they will not be able to pay. I can also imagine that it is in the interest of the health insurers to encourage this practice, and that, as a major source of income for the consultants, they have the leverage to exert their influence.