It is personal opinion on this, and possibly uninformed at that-- but:
The US has a known problem with underfunded public health, especially in terms of mental health.
This problem is caused by lack of basic service providers, and made much worse by lack of progress in finding better treatments, through lack of funding for basic research for public health, both physical and mental.
I agree that money should not be given to charlatans. However, Dunning-Krueger applies. Acknowledging this, and putting qualified people in charge of grant review and acceptance, will go a very long ways. (However, it requires people that are not competent to acknowledge that they are not competent, and defer to people who are, who also happen to be their subordinates. Yes, I know that is not how that normally works in practice, and thus is unrealistic to expect. I don't have a valid solution; trying to solve it just moves the intractable part of the problem around in a frustrating manner.)
Increasing this spending is an investment in a better future, and will reap rewards outside of the narrow issue of school violence, while also supplying the "Who pays, who decides" answer you are seeking.
As for "Who takes the fall for failures?" --- This can be part of the "understood" conditions of submitting a proposal. Your proposal, your fault if you hurt students. Politicians should love this, as it puts the fault of the failures at the feet of the "trusted experts", and thus increases the degree of care that will be taken when formulating and submitting trial programs.
Again, I am not an expert in any of these fields, and can only suggest the most general of guidelines. Specific solutions require domain specific knowledge which I do not have, and cannot bullshit my way through.