Salaries are certainly a part of it - medical staff are paid much lower in other countries.

Because they don't have to pay for their education. Governments there recognize that having lots of doctors is a public good and don't saddle them with hundreds of thousands of dollars of debt from medical school.

Doctors aren't the ones who pay that medical school bill (if they get a job). It's their patients who pay the medical school bills.

The problem of medical expenses in the US is a very complex one. It's essentially at the nexus of a whole bunch of problems with our society. Higher education is too expensive. We have too many middlemen. Strong intellectual property laws make drugs and devices expensive. Patent laws make evergreening more profitable than innovation. Intense regulatory requirements for approval make competition very limited for pharmaceuticals. The government doesn't maintain control of the products resulting from the blue-sky R&D it funds. etc etc.

This will partially ignore your attribution that the US problem is a complex multi-faceted issue (I agree with that but wanted to focus in) - you mention that higher education is too expensive and suggest that there are many other societal factors that make the US noncompetitive. This can cause an effect like we're seeing with the US healthcare market but the US does well in a lot of the more transferable industries (like software development) and I'm not seeing how the factors you're highlighting for healthcare wouldn't equally apply to all of those transferable jobs.

Software scales extremely well. Healthcare suffers the same baumol's cost disease as education and any other labor intensive industry including construction.