Let's take this very slowly for you. I'm not, and did not claim that there was a supernatural cause evidenced. Got that?
It's about the whole thing being a category error.
You using naturalistic methodology, which is what I use, is useful when we assume naturalism .
When someone makes a supernatural claim, this doesn't work because any outcome can be caused by any effect.
Got it?
Nope - you are getting is completely haywire.
Let me make it simple.
AB conflates two claims into one when he make the following kind of statement:
When we pray god intervenes to reduce climate change - or
When we pray god helps people recover from cardiac surgery
Those two claims are firstly
Prayer causes an alteration in climate change - or
Prayer causes an improvement in recovery from cardiac surgery
And a second claim about the mechanism of action, namely
The mechanism is due to intervention by god
But the second claim is completely irrelevant until or unless the first claim is proven, and the first claim makes no assumption of mechanism (whether natural or supernatural) merely there is an assumption of a causal relation between two things both of which are naturalistic, specifically people praying and climate change/cardiac surgery recovery.
So the first claim is entirely within the realms of naturalistic methods to assess. If it is proven that there is a causal relationship then, and only then, might we want to move onto looking at the mechanism. But here again we do not assume supernatural mechanistic claims, but naturalistic ones, as these the only ones we have methods to assess.
So on recovery from cardiac surgery we can look at psychological mechanisms associated with placebo, nocebo effects - this is what the study I mentioned did and found clear evidence of a psychological nocebo effect. For climate change we can look at personal motivations/actions etc that might be linked to people praying. Now I'm not saying this would be easy science, but it isn't impossible.
So we aren't in the territory of assessing supernatural claims using naturalistic methods. The first type of claims are entirely naturalistic, the second could have a supernatural claim associated with them, but we would restrict ourselves to assessing alternative naturalistic claims as these are the only ones amenable to the methods we have available.