If that were the case would the controller for that first facility hand the pilot off to the next frequency or would s/he instead have instructed the pilot as, "Frequency change approved, squawk VFR, you can try the next facility on XXX.XX?" From this end of the mike it seems to me that the controller would only hand off a VFR aircraft that was "in the system" and receiving flight following.
My approach control facility has 2 adjacent approach control facilities. Our radar equipment allows us to handoff aircraft to each other thru our ARTSIIE equipment WITHOUT being in the NAS system. Basically we are tranferring radar identification with only a call sign. Obviously there is an mode C altitude, but it has to be verified. So, if you come over to me, I need to find out that additional info that I require such as your destination and altitude.
Our SOP's only allows VFR handoffs.