Obviously his training was not the same as a dermatologist, but in comparing the two there should be an apples to apples comparison.
Physicians do not begin their medical training in patient care until they get to medical school, so 4 years of med school + 3 years of residency = 7 years of medical training/patient care. Obviously there are also doctors who train beyond the 3-year residency.
Nurses typically do their prereqs in their first 2 years of college and spend their last 2 years (60 credits) taking nursing courses & clinicals. A nurse with a BSN and no additional work experience will typically take 4 years to complete a DNP (Doctor of Nursing Practice) after graduating from college. So, 2 years of undergrad nursing training + 4 years of grad school = 6 years of nursing training/patient care. Depending on the area of specialization, some DNPs do an additional year of internship for a total of 7 years. And nursing training these days is not about changing bed pans and cleaning patients.
While the training is different, the amount of training is not as different as it first appears. I would also note that a DNP is not a Doctor Nurse Practitioner. It is a Doctor of Nursing Practice, which is different.