Being a Doctor on call can mean many different things. You have Interns and Residents who work on call so they can see enough patients to graduate. A Resident is considered a full fledged Doctor. Intern, not so much. A Doctor can also be on call at home. But they tend to get called in a few times a night. So odds are you can be on call and seeing a patient. Specially if you live in a city.
Going to the ER at night is proof of this. You can wait hours before actually seeing a Doctor.