Anyone should be able to scan their own library against the database for false positives. “But predators could do this too and then delete anything that matches!” some might say, but in a society founded on the presumption of innocence, that risk is a conscious trade-off we make.
The law requires companies like Google and Apple to report when they find CSAM and afiact they would generate hashes and add to this database if new material is found.
I don't know if there is any oversight in this. It's all done behind closed doors so you just have to trust that the people creating the hashes aren't doing anything nefarious or mistaken and that's a separate point apart from what others have said on here that you should be able to trust your devices you own to not be informants against you.
It's kind of like the PCAOB... private 501.3(c) with congressional oversight and funding.
I think the strategy is that the organization is able to do more for helping children internationally if they're not seen as part of the Justice department and the executive, which after the debacle with CBP and "kids in cages", was probably the right call.
My point is that we have no way to verify the database wouldn't be abused or mistaken and a lot of that rests on the fact that CSAM is not something people want to have to encounter, ever.