The ethically correct response if a minor should tell you that someone has been or is molesting him/her is to inform their parents or guardians of the child, whose are responsible for rearing that child as to the abuse reported to you by the minor. Your ethical responsibility is discharged once you have informed the child's parents of the crime.
In such cases reporting it to the parents is commendable, but that does not discharge the legal obligation incumbent upon anyone subject to "mandatory reporting" laws. A first-person report to the authorities designated by law is required. You cannot avoid that responsibility, you must report the situtaion.
Reporting such matters to one of the elders only wastes time
That is not the point. This discussion is not about reporting anything to the elders. The question is whether the elders, having a suspicion of molestation, will fullfill their obligation to report it to the proper authorities as required by law.
but if one of the elders is requested by the victim to report the alleged crime to the authorities -- and by this I don't necessarily mean the child, but the parents or guardians of the child -- then the elder is free to oblige.
No. An elder subject to a mandatory reporting law must make the report. There is no requirement that they be "requested" to do so, they must report. This is not a matter of "obliging" as a social grace, it is a legal obligation. Even if the parents say not to, they must report!
You seem to be asking me whether an elder is ethically or legally required to report the alleged crime (since we do not really know that there has been a crime, do we?) to law enforcement officials upon his obtaining knowledge from the alleged victim that he or she has been sexually molested, but what if that elder should unwittingly be filing a false report?
I am saying they are legally required to report suspicion of molestation as defined in the law. For the very reason you suggest, most states offer protection against claims of false reporting for any report made in good faith. For example (search result from the link in my previous post):
Citation: Cal. Penal Code ยง 11172(a), (b) (LexisNexis through 2008 Ch. 765)
Statute:No mandated reporter shall be civilly or criminally liable for any report required or authorized by this article, and this immunity shall apply even if the mandated reporter acquired the knowledge or reasonable suspicion of child abuse or neglect outside of his or her professional capacity or outside the scope of his or her employment.
Any other person reporting a known or suspected instance of child abuse or neglect shall not incur civil or criminal liability as a result of any report authorized by law unless it can be proven that a false report was made and the person knew that the report was false or was made with reckless disregard of the truth or falsity of the report, and any person who makes a report of child abuse or neglect known to be false or with reckless disregard of the truth or falsity of the report is liable for any damages caused.
If one of the child's parents or guardians is the one implicated by the minor for molesting him/her, then the ethically correct response would be to report the crime to the police, so that you do not become an accessory after-the-fact by being sworn to secrecy about the matter by the spouse of the abuser. Your ethical responsibility is discharged once you have informed the authorities of the crime.
This time you got it right. The only way to discharge your responsibility is to report the matter to the police or other legal authority. As for being "sworn to secrecy": such a promise cannot be morally justified, and there is no onus on you for following Caesar's law and God's law by making the report. Indeed, if anyone tries to extract such a promise from you, I say to include that in the report!