Odds are that the tests were designed with the cooperation of those that believe in woo woo. True believers often are so sure of their beliefs that they will subject them to proper testing. It is only when the testing shows that their beliefs are false that they turn on the testing procedure.
The worst real world example that I can think of is the Shroud of Turin. A group of scientists all agreed on protocols, where to sample from etc.. But when the results told us that it was a fake at least one scientist went back on his word. He supposedly found some threads from his testing that dated differently. The problem was that one of the protocols that they all agreed to was that of no private sampling.
That means we know that he lied. The only question is when.
Indeed, as far as the shroud is concerned what is very telling, is that the RCC have refused any further testing since to establish the date of its origin beyond this subjective conjecture offered post ad hoc.
Porfessor Dawkins had a series on TV, and they designed a test to test the claims of water diviners, it was double blind and the results duly examined, with all of the people claiming the ability very confident it would validate their belief. They all produced results either directly in line with blind chance, or even below this for some. an unequivocal fail, yet in every single case they refused to accept the results, and blamed the test had somehow skewed the results.
One can only imagine the contrasting reaction if the results had gone their way. You have to laugh really. If faith is to be admired for anything, it is it's impressive efficacy in helping people cling to a belief in the face of all contrary objective evidence.
As far as the participants in that research, yes it's hard to imagine they participated if they did not believe their prayers would work, and the bible certainly makes some fairly heuristic claims about what prayer is able to achieve.
Mark 11:24 ESV
Therefore I tell you, whatever you ask in prayer, believe that you have received it, and it will be yours.
John 14:13-14 ESV
Whatever you ask in my name, this I will do, that the Father may be glorified in the Son. If you ask me anything in my name, I will do it.
Hmm