Is this another matter that differs according to whether the intructor is working for the school as an employee or as a self-employed sub-contractor?
I am not a lawyer, but I always understood that an employer cannot seek any financial recompence from an employee who damages any of that employer's property. Even where the employee is clearly negligent, the employer still cannot claim, but might have grounds for sacking the employee.
An employee should automatically be covered by the employer's Employers Liability Insurance and Public Liablity Insurance.
If an instructor does agree to be treated as self-employed then it would be prudent to check just what he is insured for before he starts work. His biggest uninsured risk may not be damage to an aircraft. What would be the situation if a student was seriously injured or killed in circumstances where negligence, by his self-employed instructor, was alleged?