That's actually pretty simple. Equifax is the biggest provider of these types Q&A's. I'm not even sure that the company itself is exposed to the actual answers - I believe the credit bureau just responds with a pass/fail. Admittedly, it would be less creepy and more welcoming if they sent you to the Equifax website to do the verification. That way you would know that no one else actually has or will receive your personal info.
I'm not sure I believe that talking to credit report companies directly would be more welcoming. They'd probably try to charge you for the privilege of using them. In the UK they're quite known for giving out free reports, then sending you followups + charge you from the next month with no easy way to stop it (in some cases you need to sue them to stop). Not sure who I trust more - Coinbase or Experian...
They did have a blurb that said this was all "public information", but if I pop my name and car into $search_engine (for example) nothing relevant comes up.
Search engines haven't indexed everything yet. There are lots of public records that aren't indexed by google, unless they make the news or get the attention of some blogger. This includes civil judgements, tax liens and bankruptcy to name a few.
