there are certain things that sciences cannot explain.
growing up in the modern american world, i did go to church, teach sunday schools, etc...
i've worked in the science field for a few years too.
my personal experience is when i was a teenage, every time the day is sunny and has a rain in any part of the day, then right after the rain, i would have bloody nose for few hours; sometimes to the point that i had to go the hospital. when we moved up to live in the state with lots of hmong people, one of my uncles did a hmong ritual called khawvkoob when i had my nose bleeding. ever since that ritual i have never had bloody nose in my life to these days. his explanation was that my soul (plig) needed to be appeased; i remember that he just took a bowl of warm water and tap on the back of my neck, my forehead, then i took a sip of that water afterward.
i use to hate hmong rituals too. i think most part of my hating is that i did not understand the rituals, or that i did not know the rituals, they were difficult to learn as well.
another interesting thing is that one of the hmong medical doctors became a hmong shaman as well. he became very sick and the elders said he has to become a shaman in order for him to be well. since he became a shaman, he's not sick.
It could very well be a coincident.
Hmong people are notorious for associate an event as the cause of something.
See a snake in the house and a month later a child die, the snake cause the child to die.
In your example, the shaman did something and the girl got well. But it doesn't mean it was the shaman that made the girl well. It could very well be that the girl just got well at the time the shaman did what the shaman did.