The issue really surfaces when you dissect "statistical training". I had a conversation with a colleague getting the a PhD and about to publish a paper. She was mentioning to me that she tried "a bunch" of different specifications and the one that was significant was [I forget what the variables were, but this is in the education field].

I pointed out to her that, since she tried a bunch of specifications and chose the one which yielded the "positive" result, wouldn't that fundamentally alter the interpretation of the p-value, and possibly invalidate her claim?

She looked at me like I was a moron, uneducated, and trying to be difficult.

I'm forever indebted to my econometrics professor who helped me build a tremendous mental model about how to think about these issues. But between the really poor training (most people I encounter in the field just run STATA/SPSS commands with limited/no understanding of what they do mathematically) and the terrible incentives facing researchers (you don't see many negative results published, do you), it's no surprise that when people come in and attempt to seriously replicate even foundational findings, they often come away disappointed (thinking about the Reproducibility project - https://en.wikipedia.org/wiki/Reproducibility_Project)

I, too, don't have an answer to this. But I can only imagine that the way to prevent is to push the industry in the direction that truth-seeking, not novelty, is rewarded. I've mentioned this before here, but I know professors who established their entire careers on the backs of research which was later completely refuted -- even in cases where their actions where fradulent. And they are still teaching -- and successful.

As academics - like media and enveryone else -- are chasing our ever-dimming attention spans, I think this'll be a really tough nut to meaningfully crack