They do not. Their "network" comes from scraping resumes from Monster and similar sites.

They store this database of resumes and addresses then send out a wave of emails for every next position they get, then process the replies from whoever replied to those mails and there you have your candidates.

I found that unsubscribing from those staffing firm mailing lists doesn't work but in some cases. In that regard UK agencies seem to be the worst of the bunch. Eventually I had to report those emails as spam and after a while the spam filter learned to catch those email automatically saving me the trouble.