Over the last twenty years in UK jets I have often come across apparent evidence of communication between Chief Pilots and Ops Directors.
I would say that it's not as 'organised' as described above, but 'annecdotal references' can and do get passed between companies. In general I would never trust that I am making a 'confidential application' to anyone.
A few Chief Pilots are infamous for phoning a pilots present employer and asking for an unnoficial reference, the present incumbent at easyJet holding the dubious honour of being the most prolific at this game. However internet applications and use of an agency seems to have reduced the number of complaints that have made it to my ears recently.
A simple rule is to trust no-one, and make your friends in the Air Force, because you are going to need them for the rest of your career!