Another issue is that for some types of training the plane has to be maintained to certain standards. And the owner might not be maintaining the plane to that specific standard, but to a lower standard that's adequate for his needs.
From memory (but correct me if I'm wrong), ab-initio training requires the plane to be maintained to Public Transport standards.
Furthermore, you may want to check whether the plane is insured for ab-initio training. Possibly the instructor plus the student (for solo flying) have to be named in the insurance documents as covered PICs, and there might be increased premiums and/or an increased excess for this type of training.