They Check the box, then the screen agent takes a closer look, "Hmm, this nine year old indian girl named Charles Manson is probably not the 70+ year old dead man that we were worried about"
If you sign up with name, birthdate, and address, maybe the system comes up with an 85% likelihood that you're that Manson. But if you check the box, you can add in data like place of birth and SSN which prove you aren't the infamous murderer, so the system (or more realistically, a human with override powers) can clear you. That's way better than being silently blacklisted, or having each interaction delayed until it can be separately verified.
Presumably, Manson wouldn't want to check that box because he'd be likely to get arrested, and if he did then the subsequent data would all just confirm there's a problem. It's not a great system, but it's a decent improvement on just making a decision without the extra caution.