Duty of Care is a bit opaque in US Law but it is there, it comes under State Laws of Tort which does make it a bit different from most European legislation which is informed by Human Rights principles. 

Nevertheless there is clear recognition that duty of care in US non profits has a significant role, although the focus is expressed more internally than to care of those impacted by the non profit, however in practice they should amount to the same thing: e.g  https://www.councilofnonprofits.org/running-nonprofit/governance-leadership/board-roles-and-responsibilities  What it means is that the Trustees of a non profit can’t, if they are acting ethically, pretend that some uncomfortable truth doesn’t exist, they have a duty to acknowledge it and where needed, respond accordingly.

Timeless Today is a private business so probably immune to outside influence, but the Trustees of TPRF should at the very least have had a formal discussion about what the implications of the recent public revelations have on an organisation that bears the Rawat name, not least any ongoing risk: https://nonprofitrisk.org/areas-of-expertise/youth-protection/ In the case of TPRF its President especially has a duty and if family loyalty involves a conflict of interest, then the post holder has to step down at least temporarily.

Anyway the responsibility is with the Trustees and it’s a measure of their ethical standing how they choose to act – or not.