One thing about the US, is how we handle settings where one could conceptualize a contract as being needed, but where it would be way too inefficient and impractical to negotiate, write out, understand, and sign, a written contract. In those cases, which includes things like retail sales, restaurants, and may other cases, the UCC or Uniform Commercial Code[1][2] applies. Not sure offhand if that relates to the medical example or not, but I expect that at least some similar notion applies. So there are binding laws that cover these transactions, it's just not done the same way as a "full fledged contract".

[1]: https://en.wikipedia.org/wiki/Uniform_Commercial_Code

[2]: The UCC also covers other things, but these cases are a lot of what it's best known for.