I've had rosacea since my late teens. About six years ago I stopped using shampoo as an experiment: I figured it would either make my skin worse, or better. To my surprise it had no effect at all. I had super greasy hair for about five days, then suddenly it was fine. I never went back to using shampoo regularly, but mostly just to save money – I use it maybe once every few months if I've actually gotten dirty, or I'm in a super humid climate.
By contrast, what I eat and drink has has a huge effect on my skin, and the only time I've actually looked 100% "normal" was when I was drinking an enormous regular dose of Chinese herbal medicine. But later I used a topical antibiotic, and that more or less fixed it: not as thoroughly as the Chinese medicine, but close enough (and it's way less hassle).
What is the moral of this story? I guess that no one I've ever spoken to has the remotest clue how the skin works.