The rental shop alternative is the answer. If the student refuses, I would refuse to have that student in the class, until an approval from management of the ski area was obtained. If that student was hurt due to unsafe equipment, the ski area could be held responsible. I certainly would get a waiver signed by the skier, or appropriate supervising adult.
Your knowledge of the out dated and probably untested bindings could indirectly obligate the resort to suggest appropraite and corrective actions necessary to the protection of the safety of that skier. In action [ allowing that skier to continue in the class,] with that skier eventually becoming injured while in your class, a court of law could determine that the ski school and /or the ski area was in fact possibly responsible for the safty of that skier. Your knowledge of the unsafe or seemingly unsafe equipment creates a situation of possible negligence, if that skier is allowed to continue in your class on what could possibly be dangerous equipment.
So in conclusion, the continuation of the student in your class on questionable equipment, should be Ok'd by resort management. Better safe than sorrow for all the parties.