Is the client saying that he/she flew on a particular flight and the airline has responded (in truth) that they have no such record (from the pax list) of that?
No, we haven't been told anything about what the airline have said, other than the fact that they have asked to OP's client to prove they were on the flight:
I am acting for a client who has been unable to prove he was on said flight (the airline are seeking "absolute proof")
I suspect that it's simply a case of an airline, faced with a claim, playing hard ball and insisting that the passenger provides independent evidence of something that the airline already knows to be the case.
Speculating about security breaches, dodgy head counts and incorrect airline records might be fun, but I don't see its relevance here.