From what I've read, this is supposed to catch the bad thing after it happened, not to prevent it. Then you say that 1 in 1000 is an acceptable error rate. 1 in 7 billions is not an acceptable error rate!
If you catch people who have done bad things you prevent the bad things they are likely to do in the future.
1 in 1,000 does seem a bit high to me, but the prevalence of the bad images matters. You also have to think about the consequences of false positives versus admitting child pornography. If 0.1% of innocent meme pictures get removed from a site incorrectly - that's not ideal, but how much sexual exploitation of children do you need to stop to make that worth it?
When systems like this return a positive match, that doesn't result in a summary execution. Rather, it prompts a deeper investigation.