Also, while this isn't super-relevant, given that I already agree with your claim about people confusing themselves, my impression is that the link you gave presents moderate-to-weak evidence against this.

I didn't read the entire article that was linked to discussing the statistical analysis (if there's a particular section you think I should read, please let me know), but my understanding was that in some sense the "experimental procedure" was the issue, not the statistics. In other words, Bem considered potentially hundreds of hypotheses about his data, but only reported on a few, so that p-values of 0.02 are not super-impressive (since out of 100 hypotheses we would expect a few to hit that by chance).

Bem's experiments all basically ask "is this coin biased", which isn't a very complicated question to answer. It is the sophisticated statistics that corrects for the flawed procedure.