Just a thought, if the passenger checked in bag(s), the flight could not depart without either the passenger or off-loading the passengers bag(s). No record of bag(s) being offloaded, the passenger must have travelled on the flight. QED.
I suspect that's not going to help much.
In the absence of a baggage tag, which presumably would have been thrown away along with the boarding pass, proving that a bag was carried is going to be as difficult as showing that the passenger travelled.
The issue isn't about whether the airline will have a record - they obviously will - but about whether it would be possible to supply independent proof, though frankly I still don't see why that should be necessary.