> This particular plot is a statistical smoking gun, and suggests that the positive results from the original studies (black dots) were probably the result of p-hacking. They were chance findings, selectively published because they were positive.
From that, it seems to me like the problem isn't what the researchers published, it's what they didn't publish.
I'm a programmer, not a researcher, but in college chemistry we had marble notebooks that we wrote everything down in. The notebooks made it obvious if a page was torn out, everything had to be written in pen, and if we crossed something out, we had to cross it out in such a way that it was still legible. If we didn't include data in our results, we were expected to explain why. The most valuable thing I learned in those classes was the importance and practice of auditability.
I doubt that my classes were unique in this respect and I wonder if this might be the solution to the problem. I've long been a proponent of people simply publishing literally all their data now that internet hosting is so cheap, and only publishing syntheses of the data in journals, giving anyone the opportunity to verify the author's conclusions. Psychology is different due to the need for confidentiality for the people being studied, but the full data should be available to at least the peer reviewers before a study can be published.
EDIT: To add to this, elsewhere on this thread there's a lot of discussion about people not publishing negative results because they're not interesting. But reality doesn't have a bias towards results that are interesting, only humans do. I don't know how to solve this problem, but at least making publication of your non-interesting results a condition of publishing your interesting results would be a start.