Prayer does work in a way, if you believe it does, because your mind has powerful influence over the body. You can, quite literally, will yourself sick; much the same, you can will yourself to heal... but you must believe it 110% with absolute conviction.
HOWEVER
This is NOT a substitute for modern medicine. The body is an INCREDIBLE machine capable of repairing ENORMOUS amounts of damage and overcoming TREMENDOUS attack by foreign invasion... but it has its limits. Why one would ignore conventional medicine in favor of a prayer only approach when conventional medicine has a near hundred percent recovery rate on the disease in question just staggers me... these people were incomprehensibly stupid!