I personally believe that as an instructor it is our responsibility to supervise our students until they have their own licence to operate the a/c. Until that time, we are supposed to be 'teaching' them.
At what point aren't we teaching them, even when they're solo? They have our permission and the skills they have, come from our methods of passing the knowledge across.
If the student messes up, isn't it our own failing as an instructor?
I would believe in this instance, the instructor is at fault as he should have been there to supervise the start and if he disagrees with this, then should he really be in the position of instructor and signing for an a/c under his control?
I believe the training facility in question here is more of a trial lesson factory anyway, and emphasis is put on how much money they can make from each student in whatever way possible. Whether it be from selling headsets or selling helicopters, the bottom line is 'can we fleece them for a bit more cash'?
All open to interpretation I guess but individual FTO/RF rules etc are rarely read by students. Please correct me if i'm wrong.