Apparently, people who pray experience some health benefits over people who don’t. This may be true, and can be explained without resorting to God or religion.
The more contentious question is whether a group of people praying for a third party can help that person.
There have been studies about this, mostly showing not much difference between being prayed for and not. And there was one famous study showing that people who knew they were being prayed for did worse than those who didn’t know that they were being prayed for.
But the guys on the podcast (and maybe the article – I didn’t read it) point out the big issue:
How can we measure prayer? For example, let’s say that some researcher got a group of people to pray for the recovery of patient X, but not for patient Y. The idea is to see how they recover, but how can they be sure that other people, outside of the study, aren’t praying for patient Y?
In fact, there could be people praying that patient X does NOT recover. How would that affect the study?