Typically recruiters just use adverts to obtain CVs to put into their CRM system and match them to a range of roles they have available. The specific role you apply for isn't that important to the recruiter, as once they have your details they'll try and match you to any job they have which they think might be suitable.

The cost of advertising (which is high) is amortized by the long term value created by the CV database. Giving third parties access to those CVs is something I would imagine most recruiters would be reluctant to do.

Just about every role I've sent to a recruiter appeared within a few hours on the normal selection of websites - I'm not sure they ever had anyone "from their database" although they claim that.