Dublinpilot, I would add one: when the local pilot is doing the radio, or is dealing with authorities on the ground; for example where the PIC does not speak the local language, and knowing local customs can be vital for keeping the aircraft from being impounded, "fees" being imposed etc.
Odai - I would NOT rely on local rules who can log PIC and not. The rules that apply to you are the EASA rules. What the safety pilot logs is his problem. I have two completely different total PIC times, depending if EASA or the FAA ask.