For me I think it would depend. During cruise over the UK with airports all around I would be tempted to call a PAN (knowing that ATC in the UK would understand this). During t/o or cruise somewhere remote I would say mayday.
About Superpilot's CRM instructor's story; In the back of my head something says that only a PAN should be used whenever it is not your own vessel in danger (regardless of the level of danger). Anyone know if I have actually read that somewhere proper or if I am just making it up?