Exactly where you typed It means that a quarter of the published papers say "Hey, we did this experiment which offers conclusive proof of X"
Again, this is patently false because they did not publish papers claiming conclusive proof. They published papers claiming evidence in favor of a theory.
>Make up your mind already.
There's no reason to be disrespectful over a mistake. I meant 1 in 20 (5%, hence the mix-up).
Returning to the point, it takes incredible mental gymnastics to argue that a false positive automatically degrades the status of a study from "scientific" to "unscientific":
1. The adjective "scientific" describes a method, not a result. Those speaking of "scientific results" are either (a) referring to "results of a scientific study" or (b) confused about what science is (namely: a method, not a result).
2. A false positive degrades the status of a result (not a study) from "evidence in favor of X" to "not evidence in favor of X".
I must respectfully insist that you are wrong.