This legal stuff avoids the issue: health aid free at the point of supply, for all a country's nationals.
Having to go to lawyers hardly forms part of what normal health experience is. Do you have to be hit by a truck in order to get attention? What if you just break a leg at home, do you go to a lawyer and sue yourself to get help? Do you hire a lawyer to find some other patsy you can milk or blame for your own stupidity? Bringing in the concept of claims against somebody because of injury is a separate subject, in this context the reddest of red herrings.
What we are - or should be talking about - is access to a medical service in case of illness, not necessarily of accident. Different concepts and situations, but in either case one should expect medical help without a credit card or a legal eagle. That many look for those commissions is not surprising, as equally unsurprising the fact that health insurance is so high just to protect insurance companies from marauding legal sharks looking for somebody's disaster to convert into their Bentley.