It doesn't really guarantee uniqueness. It also doesn't verify identity (that this is really "John Smith"). It essentially verifies that the user has paid for an account on RealPerson.io, which is currently $9/year. This was to strike a balance between having to divulge too much personal info to RealPerson.io (like an identity verification service), but at the same time making it highly unlikely that the user is a bot. RealPerson.io doesn't try to drive the percentage to 0 that the user is a bot, but rather make it cost prohibitive for bots, while at the same time making it cost effective for real people, and still protect privacy.
Also, a user only gets one RealPerson code per website, so a user can't create multiple codes for a website and hence create multiple accounts on that website. And if that website bans the user, that user would need to get a new code for that website, which would mean creating a second account on RealPerson and paying again and face the scrutiny of RealPerson detecting that the user has two accounts on RealPerson.
Also, a user only gets one RealPerson code per website, so a user can't create multiple codes for a website and hence create multiple accounts on that website. And if that website bans the user, that user would need to get a new code for that website, which would mean creating a second account on RealPerson and paying again and face the scrutiny of RealPerson detecting that the user has two accounts on RealPerson.