I believe the present state of affairs is that you do not have your passport stamped, but it might be a good idea to ask for this as proof of when you brought in the vehicle. As to flying out I never used to have any problem even in those days they did stamp your passport with vehicle details.
I can't see it as a problem now e.g. what if your car wrecked in an accident, impounded in garage, illness back home or a whole host of other things that require you to travel without it. I don't think they would ask 'where is your car'. It's only the police on Corfu when seeing your car might say 'how long has it been on Corfu i.e prove when you brought it in not when you take it out or it no longer becomes yours?
However if you have gone over the six month period that might be a different matter.