This can only be a patial explanation of the effect since it is known to occur even when the patient is informed that the substance is inactive.

https://en.m.wikipedia.org/wiki/Placebo#Mechanisms

Maybe there is something akin to belief in the belief, i.e. "I'm not religious but will pray for god or whomever in dire situations". The mind is a weird thing and truth is, we don't have a good understanting of what's going on with the placebo effect.