I've been going over this back and forth and I'm still confused. The multiple studies in each article are generally designed to observe the same phenomenon manifested in slightly different ways. So how can the authors treat them as independent events and simply multiply their probabilities of success to compute a cumulative probability? Am I missing something?
The conclusion is also very puzzling: you have to show some studies do not find significant effects in order for your set of studies to be statistically credible. But when you do, your theoretical rationale is then questioned. So you're damned if you don't replicate and you're also damned if you do?