I attended OBA many years ago I am ashamed to say, and on induction the you had the option of paying $100 dollars "damage to hull" insurance which most people signed up to.
Recently I am pretty sure OBA were forced to cease trading by county inspectors due to them not having adequate insurance in place.
Regarding medical insurance a normal travel policy will noy cover you for flying training, I took out an aviation insurance policy from trafford's insurance, which was recommended by OBA which would cover any illness or injury sustained while training abroad. It was similar to a policy for a ski holiday or any other extreme sports trip which is not covered in your normal two week package in the sun travel policy