Some of these religious nutters are relying on a "belief in God" or "faith" to save them from their ills, including some very serious diseases.
What they are, in fact, relying on is the placebo effect. If the mind is tricked enough into believing that the body is going to get well, it can have some benefits, especially in overcoming limiting beliefs such as shyness, fear of heights, etc. or at least make the patient happy while their body heals naturally.
However there is a reason why medical trials include placebo sugar pills against the actual drug to be tested... and that's because placebos DON'T work against disease!
Derren Brown did a TV special on the placebo effect. The show's second part was pretty much the final word on why religion is bunk, and why people still believe in it anyway.