Yeah I agree caution in interpretation is important.

However, given enough scientists all three forms of false are being published in parallel (as well as genuinely true results), which is the key problem. Without bounds on publication bias and publication quantity you can't really rigorously associate a probability of truth from a p-value* in isolation.

(hmm, I suppose meta-studies are a kind of remedy to that so maybe it will all work out anyway)

* or whatever