When I was checked out on the Arrow, I just got the "official" club checklist and weight & balance info, plus a verbal briefing.
When I was checked out on the Bulldog at another club, part of the procedure was a written exam paper covering all sections and procedures, which could only be answered by reading the POH. The POH was also kept in the aircraft.
I know a lot more about the Bulldog! I think clubs are reluctant to release the handbooks with so many different people flying the aircraft they could easily go missing. For a group it is a different matter.
RD