Now, I'm not one who bandies about the term "miracle" lightly - nor do I consider the birth of a baby to be one - that's a natural order event. However, once you study this disease, its easy to see that there is no coming back from the stage this victim is alleged to have....barring divine intervention. Unless you are one who believes that science can and will cure everything.
But, I don't doubt your consideration of the "prayer thing" to be silly. You wouldn't be the first.
I don't think you know as much about neurology as you think you do. These doctors weren't just throwing darts -- they had a theoretical reason to think that the treatment might work, and it did. Anyway, time will tell, and probably not very much time. No doubt this technique will be tried again on the very next symptomatic rabies case in a developed country. Most likely, this treatment will become standard and fairly reliable.
I'm sure there were people who insisted on attributing the amazing early results from penicillin to divine intervention. But alas, it was the mold.