In "Safe Harbor," what suspicion does David have about the worker outside the clinic in the beginning of the story that is borne out by the man's remarks near the story's end?

At the beginning of the story, David sees an exterminator working outside the clinic and wonders if the man thinks that he is a patient in the facility. Near the end of the story, as David is trying to leave to go see his mother in the emergency room, the exterminator asks him whether he should be out in the front parking lot, indicating that he really does think that David is a patient.