I know I'm a bit late to the party in discussing the latest attempt to see if prayer conforms to the scientific method. I still feel like chiming in.
Here's my beef with it. You're talking about attempting to apply the scientific method, which works splendidly for non-sentient forces like gravity, onto a sentient, independently operating entity. It's like attempting to predict humans. You can get autonomic and reflex behaviors pretty well down, but when it comes to the softer stuff, like emotions and whether you can get your neighbor to feed your cat, there are variables science can't eliminate. The will of a deity to act like a performing seal has to be even slipperier than black ice. Frankly, if I were a god and knew those prayers were being done purely in the name of proving my existence, I'd have a bit of fun with it so long as the results didn't mess with the broader picture. And I rather doubt the Christians' god is above such behaviors himself. I respect him as much as I do any god I don't have direct allegiance to. I just find that most gods I deal with like to have their occasional joke. I've seen no evidence that Jehovah's any different. He's just as slaved to the web of nature as the rest of us, too.
The only way I think any prayer studies will ever be trustworthy is if they manage to find a situation in which the targeted deity is required to answer. I don't think that's going to happen.