See, that's exactly what Popper referred to when he said that theories cannot be confirmed, only rejected. Simplified to that extent, it's not nearly correct, but apparently we need to simplify it even more to get through the thick skulls of people like Bem.
The theory Bem et.al. refuted is "ESP doesn't exist and if ESP does not exist, there is no effect in these experiments." That's a much bigger theory than "ESP doesn't exist". And indeed, every single time somebody purported to have evidence for ESP, it turned that the typically tiny effect was a flaw in the experimental design, be that due to fraud or incompetence.
> obviously that is bullshit
No, not at all. Nothing is obvious. It's bullshit by sound reasoning.
There aren't just two theories that are competing here ("ESP" and "no ESP"). There's also "this researcher is incompetent", "this researcher is a fraud", "these statistical methods are useless", "I'm high on crack and none of this real", etc. A priori, "ESP" and "no ESP" might be the most believable among those, but all the past evidence points strongly towards a combination of "this researcher is incompetent" and "these statistical methods are useless". That's why we can say that this is bullshit and not feel bad about it.
> if obvious bullshit can make it through the scientific process
A pay-to-play journal like F1000Research is part of the scientific process? That may be where your confusion comes from.