I’m familiar with Rav Klein’s opinion, and it definitely appears to be in the minority.
Rav Dovid Cohen says, Go to the police. Rav Hershel Schachter, of RIETS, who is respected in the yeshivish and Chassidish communities, says, Go to the police.
I don’t believe the type of burden of proof you’re insisting upon is actually being followed in the vast majority of battei din today where child abuse cases have been adjudicated, in the recent past. There have been special battei din dealing with these cases in Los Angeles and Chicago, for example, where rabbis and professionals have worked together, and they could not have applied the ultra-high burden of Torah law that existed in the past, i.e., two witnesses, and warning.
Another example is a case heard by Rav Shmuel Kamenetsky, written about in the Forward. There was victim testimony only, he was persuaded by the testimony, and he forwarded his findings to a beis din in Eretz Yisroel. They decided not to pursue the case, because they felt it was too old. The important point here, however, is that the strict Torah rules of beis din were relaxed. If not, we’ll have child abusers running amok, which, to some extent, is what is happening.
Yes, it appears that the questioner was asking about a specific case, but the factual details are omitted from Rav Elyashiv’s opinion. That’s critical. As a result, we don’t truly know what evidence would satisfy Rav Elyashiv. I read the “p’sak” more as a guideline, than as a definitive halachic ruling. There are other teshuvos where the evidence is specifically referred to. In secular law, there are also appellate court precedents where, in discussing burdens of proof, specific evidence is referred to.