Earlier quoted context omitted.
Healthcare is cheaper in every country everywhere regardless of whether they have public or private coverage. This implies that the difference isn't public vs. private, it's some other regulatory differences which are driving up costs in the US.
… it's some other regulatory differences which are driving up costs in the US. It suggests regulatory capture and/or lack of proper governmental oversight.
"Lack of government oversight" almost never leads to high consumer prices. It can lead to externalities, but if there are no regulations preventing anyone else from competing with the incumbents, it's very hard to sustain monopoly rents.