Given the kind of burn rate those people have at government agencies I would guess that they have some form of partnership with aforementioned agencies. I glanced through their FAQ and site but didn't see anything specifying that however.

Other than that I have no idea how you would even be able to have the images to classify in the first place without running into problems.

To build a classifier, yes, you are correct. But this isn’t a classifier to identify new content that has never been seen. This uses perceptual hashes to help organizations detect if known CSAM is being shared on their platform.