The easiest thing to remember is it is a kick until and unless possession is gained or it rolls to a stop. It makes no difference who touched it (kicking team or receiving team) if possession is not gained before it crosses the goal line. As soon as it breaks the plane of the goal, it is a touchback and should come out to the 20.
TideHead, you are right about the insurance policy unless, as Jref said, the receiving team commits a foul. When the kicking team touches a punt, the spot should be marked with a beanbag. The receiving team can then pick it up and take off and, if they fumble and the kicking team recovers, the receiving team can go back to the spot of first touching and take the ball there. If the receiving team commits a foul such as blocking in the back, holding, etc., then the first touching is ignored.
In the play that you described, the receiving team should have been given an option of taking the ball at the spot of first touching or the result of the play which would have been a touchback.
