Similarly, among the people prayed for and who recovered, were some of them "naturally" in better shape, merely because they were already healthy enough to be regularly attending church, had a large support group, etc.? It might be that a group of gregarious people and a group of sullen loners would exhibit wildly different health statistics, prayers or no prayers. In other words, it's difficult in such studies to avoid playing with a stacked deck.
Indeed, in any such formal study it must be much easier to collect the information than to understand it.