Music is one example.
What information about the universe do we acquire from music?
If someone claims to have been cured then we can scientifically investigate if such cure indeed had occurred. But we can't put a scientific evidence about the cause of such cure.
Of course science can investigate such claims. It belongs to the scientific field of epidemiology. In fact the pro-faith Discovery Institute did exactly that. Turns out prayer for healing doesn't work. It's not for you to tell scientists what they can and cannot achieve. If god acts in the world he is fair game for the scrutiny of science.