The study's goal is to see if they can objectively measure the effects of prayer. Since it's commonly believed that prayer can help heal the sick, they chose that as the basis of their experiment. Everything else appears to have been designed using the usual sorts of scientific controls. If the "God vending machine" delivered the goods more often than random chance, then they'd be able to measure it.

Of course, the absense of any measureable response says nothing about the ability of a sentient supernatural being to cause measurable effects. Maybe God doesn't much like being measured. (Striking down the scientists with lightning or aflicting them with locusts or something might also be measurable, thus the apparently lack of any observable supernatural effect.)