To me Unit Testing is more about testing the expected outcome and making sure of the status quo rather then finding bugs and testing all the extreme small edge cases. Then when an abnormal and unexpected situation occurs, writing a test that induces it and fixing the code so that all the related tests pass.

To use the doctor analogy, I would say unit testing is more about testing patient outcomes when they are put through varying courses of drugs or treatments (fixing bugs and adding new features) rather then trying to make them die before declaring them healthy. Is the patients blood pressure normal? Check. Now the patient wants to start some treatment for something else. Oh wait, I'm getting an abnormal blood pressure reading.