A couple of times recently providers don't want to use 411 but instead have asked me to provide identifying information.  Then they txt something like, "Thanks, now I need (for example) 24hrs to verify you".  My question is what exactly are they doing to "verify" me?  

Maybe they are running a name search in LexisNexis?

Who are you talking about?

There are services out there that will get someone's personal info based on a name/DOB. Things like work history and criminal history. Whether you're a registered sex offender, etc.

There are also provider only sites where he mysterious "blacklists" are, so I'm sure that's checked too.

Keep in mind you're likely not the only one she's working on, so it's not like she's spending 24 hours just on you. Plus she has a personal life.