Let’s first find our common ground. If you are a doctor and a patient comes to you, and the doctor refuses on the grounds he will not be paid enough, you think you have the right to compel this doctor to perform the service anyway?
The emergency care example you give is an extreme and shouldnt be used as the basis for all other policy. I would say a doctor who chose the job as an emergency care provider acknowledges your stance when he took the job, to provide service to matter what, not because it is a right but a contractual obligation.