I think the point you might be missing here is that prayer didn’t make things better.
Also citing a study without noting the specifics of that study (population size, quantifying and equating the ailments, time frame of the study, what prayers were being said and to whom) dramatically limits the usefulness of that study.
Behold, the bird the pelican…. He holds more in his beak than his belly can…. He holds enough in his beak…. To last him a week…. But I don’t know how the helican.
A 4 year-old asked her mom, " Where does poo come from?" Mom thought for a moment and decided that maybe her daughter wasn’t too young to learn about her body so she went into a detailed explanation about how important it was to chew carefully to help digestion and how it finally ended with going to the bathroom and expelling a good healthy poop. The daughter, visibly shaken by this explanation, then asked with a shaky voice." What about Tigger?"
Methinks tales are being told and legs are being pulled.