Well, the doctors who say that do exaggerate a bit.
For one thing, melanoma (a form of skin cancer) can be quite fatal. It can also be treated successfully if detected early. I personally know someone who had skin cancer successfully removed by a dermatologist. I also had a friend who died of it, much to the surprise of those of us who knew him (but did not know about his condition).
It is also not quite true that no skin disease is curable. In my twenties I had very bad acne. I went from dermatologist to dermatologist, all of whom prescribed topical solutions that helped a little but did not cure it. Then I went to the professor of dermatology at our university. He just took a quick look at me and told me to get my stomach acid tested. I had it tested by Slovakia's best experts in the field. The test showed no acidity in my stomach, something even the expert said he had never seen before (yes, I was retested several times for their research, so it was not a lab error).
I was diagnosed with atrophic gastritis and treated. Immediately, my acne was gone and never reappeared since (I am fifty now). One might argue that my problem was not dermatologic per se, but it was causing a dermatologic condition, it was discovered thanks to a dermatologist, and it was cured successfully.