Are doctors allowed to say they are "too busy" to see a sick patient?

My grandma felt a numbing headache and wanted to see her PCP right as he is getting off work in his own clinic. She called his office and asked him to stay and wait for her, but he told her to just go to a hospital, and that he was "busy" and could not see him. Previously he had told her that he could make house calls if she is sick.