It is absolutely caused by a deficiency in Vitamin A. So are lice, goopy runny eyes and a myriad of other skin, eye and reproductive problems.
Since I started supplementing Vitamin A some 40 - 45 years ago, I have not had one case of rain rot or lice(except in incoming horses).
I used to breed over 100 visiting broodmares every spring. I quit treating rain rot topically and treated it with Vitamin A and found it cleared up immediately. Mares also cycle earlier and breed better and I have not had a retained placenta on a single mare since I started supplementing Vitamin A.
You cannot give rain rot or lice to a horse with a healthy immune system and you cannot clear them up without enough Vitamin A and good immune system.
The fastest way to fix it is is to give a horse the injectable sold for cattle only give it ORALLY -- DO NOT INJECT IT. 5cc orally once a week until grass is green or a good Vitamin Supplement like Mare Plus made by Farnam will fix it.