I cannot explain the reason for the dead battery but failing to turn off the A/C had nothing to do with it.
I too have your FIL’s habit of turning off all switches prior to shutting down the engine, but this habit comes from the olden days when you needed full battery power to start (especially in winter). Anyhoo, leaving accesory switches on overnight does not tax the battery at all. The electric power is controlled by the ignition switch. No ignition, no drain on battery.