Within the confines of a school the instructor has more control over access to the aircraft. But what about someone that purchases an aircraft for training and then finds an independent instructor to teach him. I can put conditions for operating in the logbook but I have no actual control over behavior. I had a case where the student was illegally flying solo without an endorsement. Another in which an instrument student was illegally filing and flying IFR in the system while I was conducting instrument training. The first situation was brought to my attention by a CFI friend that witnessed it, the second I suspected and confirmed with ATC. The instructor's liability can only go so far.