I've no idea what the answer is to the original question (DFC's probably nailed all the relevant points) but the general topic of student starts and shut-downs is a good one. IMHO it's like everything else: a balance of risk versus benefit.
Once the stude is judged able to do the pre-flight check most of us would probably leave them to do it unsupervised with the odd check question from time to time - risk that they may miss something but benefit from development of confidence and captaincy. Once I've judged them able to start safely I would normally leave them to start unsupervised; likewise once they've shown themselves capable of taxying and refuelling I would also get them to do that too - yes there's risk that they may screw it up but there's also significant benefit (again) from development of confidence and captaincy.
I also tend to leave studes to do the shutdown, but a couple of weeks ago I hopped out (park brake on) and looked back to see the aircraft slowly trundling forward - fortunately the stude woke up but I felt pretty helpless for a few seconds!
We can't remove all risk, we just need to make sure that the benefit outweighs the risk; just like every other action in life.
HFD