RTzero: correct!
While there'd be local rules, non-aviation based, that a job/assignment reference is a duty of the employer (assuming you had an employee status in the first place), it does not cover the no-accident/incident statement or hours flown.
What I heard and came to verify, that somewhere under the AOC holder approval is an obligation to give their departing crew an experience certificate.
Just like you said, a job reference could be provided (a very reasonable one) by the agency, but the airline themselves refuse to issue the flight hours certificate. Are there tools to go via CAA and push them? That's what I am after.