First thing to say is that the world has changed since Jagdeo was allowed free reign and there could be now (with very rare exceptions) no excuse for any person holding a Trusteeship not to ensure that current/recent abuse was reported and for the organisation not to make public the actions it has taken in response to the abuse.
Historic abuse is more problematic and many of the legal entities that protected Jagdeo for example no longer exist. I think perjury would only come into play were there to be a court case, and without a legal entity to sue that it is likely to be difficult to achieve.
As you say, in the US especially, mandatory reporting is a big thing, I don't know the US law in detail and I'm unclear how it applies to historic cases rather than present threats to a child.
In terms of process, an internal review might be warranted as an initial step - and for a diligent organisation that might be sufficient to produce appropriate action. Clearly an internal review that says ‘nothing to see here’ is wholly inadequate. The obvious conflicts in the Rawat orgs require at the minimum bringing in external advisors and both acting upon and publishing, that external advice.
Any organisation that has contact with under 18s should have stated policies on child protection – these would include minors being protected from exposed to any individual who may be threat to a young person’s well being. Any indication that these policies have breached should trigger an investigation, and based on that the organisation should be able say either, based on external advice that they consider there to be no danger to children, or that following information received and advice taken – “the following steps have been taken”.
This seems like pretty good over view of what would apply for example to TPRF: https://www.gg-law.com/gg-legal-faqs/child-abuse-legal-overview-of-nonprofit-responsibility/
The California Attorney General’s Guide for Charities also makes for interesting reading (more so than SoS material) with notable references to duty of care and fiduciary duty: https://www.oag.ca.gov/system/files/media/Guide%20for%20Charities.pdf
