I think it ultimately boils down to persuasion and the environment. When you're surrounded by 'faith', you can pin a lot of things onto that -- much like how some folks buy into horoscopes, homeopathy, statues, prayer cards, etc.
I know someone who considers themselves to be really lucky because they win a lot of contests -- but they only win a lot of contests because they enter a lot of contests.
I used to have warts on my hands and feet when I was a kid. It wasn't bad, only one on a finger and two in a benign spot on my feet. But they were very persistent for many years. I never saw a faith healer, but they still fell off on their own one day, never to return again. I had actually completely forgotten about that until I read your message, likely because it held no significance for me. The coincidence of faith healer + warts falling off appears more significant that warts falling off with no apparent instigator.