Doc Holliday was indeed a dentist and not a physician. In the Old West, however, remote towns often had to use what they had for medical care. Physicians were scarce, so if a town did not have a doctor they would go to the dentist, veterinarian, or even barber for care. Also sometimes physicians would be called upon to care for sick animals if needed. It is therefore not that far of a reach that a dentist would serve as the town doctor.