Is that just a reflex response though? I would expect people to be more deliberate in their interactions with medical professionals, but I can easily imagine hearing “How are you?” and my brain goes on autopilot.

Yeah, this is something I had to learn over my teenage/early 20s years. "How are you?" Is often not a question but just a generic greeting like "Hello" or "Nice to meet you". Sometimes it is though, but that's just one of the many examples of unwritten rules about how to tell whether someone literally means what they're saying or if there's a better way to interpret it.

Having only lived in the US, I don't have nearly enough firsthand experience with other cultures for me to be the one to comment on them, but I suspect that every culture has some things like this where the actual intent of the communication isn't direct. I suspect that if people in tech were asked to identify which cultures they considered to be the most direct in their communication, American culture probably wouldn't be ranked first. Generally the stereotypes of other cultures that are perceived as more direct get described in more pejorative terms like "blunt" though.

The greeting is generally in the waiting room. I’d do exactly the same if I was them.