An interesting thread and a variation on the much discussed "divemaster liability on a boat trip/is he responsible even if he's not working, etc." All the talk of lawsuits (especially in the U.S.) and who can ever prevail makes my head spin. I will throw this in: If a dive instructor can be successfully sued when a now certified former student of his has an accident wouldn't that mean anyone having a car accident could sue the person who supervised his road test?
There is a slight difference in the scenario your bringing up. Anyone can operate a car on private property. With that in mind a kid can learn to drive a car long before he ever gets to a driving test by driving in a parking lot (Unless told otherwise by the property owner either through posted signs or verbally) or any open space suitable to operate a car. The student in theory learns how to operate a vehicle with the aid of parents or anyone else brave enough to let them operate their vehicle. They then go to the testing agency which in no way demonstrates the driving skill nor forces the person to sit in an hour long lecture. If the student passes it would have been because he practiced with someone other then the tester. This for the most part limits the testing agencies liability because you showed you knew how to drive not they taught you how to drive.
Diving is a little different. For example I take a peak performance buoyancy class from an instructor. Instead following the standards he just has you do a real quick fin pivot and says you did well and you passed. Now you get your card and you run down to the oriskany which requires a mastering of buoyancy and you over inflate the bcd to try to get neutral and start to drift upwards. You then panick and dont deflate and as a result you get bent then they could go after the instructor for signing off you mastered the skill and provided the diver with a false sense of security that ended up in him being either killed or permanently injured. You are in this example stating that you showed a diver how to do the buoyancy and he showed he was fully capable when in fact you knew he had not demonstrated fully he had mastered the skill.