Ben Torah, Wikipedia is not perfect, but this particular passage is footnoted with references, it confirms what I wrote above, and I suggest it should work for now, and this is what I copied and pasted:
“A 1992 meta-analysis suggests that false allegations represent between two and ten percent of all allegations.[6] False reports are more common in custody disputes.[15][16][17] Children appear to rarely make up false allegations of their own accord[18][19][20] but will make false allegations if coercively questioned by individuals who believe abuse has occurred but refuse to accept children’s statements that they were not abused (as was common practice during the satanic ritual abuse moral panic).[7]”
In our community, the psychologist Dr. David Pelcovitz has publicly stated, over and over again, that false child abuse claims are very rare. He is a frequent lecturer, and specializes in the treatment of abuse victims.
You make a Talmudic argument: “You wouldn’t know what percent were false claims; only what percent were later proven false. Those false that resulted in a false conviction, your stats will still show as true.” Only in Shamayim will we know which convictions, if any, were false. Meanwhile, here on Earth, Jews and b’nei Noach are required to establish a justice system. Your argument does work in the beis medrash, but not when we’re dealing with life-and-death. Child abuse is a type of slow homicide. MRI brain scans and other tests have been performed on deceased child abuse victims. There is brain damage, and cell changes. Their life spans are statistically shorter. They suffer higher percentages of severe depression, alcoholism, drug abuse, and suicide. Dr. Michael Salomon, a psychologist, addressed this issue at our Brooklyn conference on October 24 at R’ Gershon Tanenbaum’s shul; and Dr. Nachum Klafter, a psychiatrist, addresses this issue in our Jewish Board of Advocates for Children Position Paper (jewishadvocates.org).
Next you write, “Furthermore, the psak from Rav Elyshev is that it is ONLY permissible to report to the secular authorities after it has been 100% ascertained as factual.” From the English translation above, which I’ve seen before, Rav Elyashiv does not insist that the burden of proof be satisfied 100 per cent.
100 per cent is also not the burden in a secular court; nor in a beis din, where child testimony is now accepted, and also women’s testimony, and you don’t need two witnesses, and warnings.
Credible victim can be adequate, particularly when accompanied by other proof: e.g., did the victim complain shortly after the crime, was there medical and/or psychological treatment, were there other credible complaints about the alleged perpetrator. Physical and scientific evidence are not required in order to get a conviction.
I also point out that Rav Elyashiv was speaking in general, not as to a specific case in front of him. I suggest the Rav was giving general guidelines, and not hard-and-fast rules. As you probably know, perhaps better than I, a p’sak dealing with an actual, live case in front of the rav-posek should be given greater weight than a general commentary. I heard a good shiur on this once, dealing with an agunah, but can’t recall the details.