My wife has psoriasis, she has recently (ish) switched to a plant based diet, her psoriasis has cleared up too. She isn't making claims that her change in diet fixed it.
Very possible, but diet changes usually go hand in hand with other lifestyle changes too. It could be any one of them or a combination, and it can also be person specific.
If she is plant based now, she could have only been SAD before? This is the reason why vegans and vegetarians think their diets are good, because literally anything besides the SAD is an improvement. She is a reduction in symptoms because of a reduction of sugar and other things. Put her on carnivore for a month and if she doesn’t experience anything I’ve described then I’ll eat my hat.