I would use it as a learning opportunity. Be honest with yourselves, is there a little bit of truth behind what the coach said, even if to a lesser degree? If your coach thought your son was a leader of the team, coach would have been in contact with him the past several weeks to run the offseason workouts, reach out to the potential players to make sure they attend coach's offseason team meeting, have been named captain, etc.
If there is some truth to the coach's words, or he hasn't been asked to lead these activities, I would sit down with my son and say "You can have all the baseball skill in the world, but being a leader, a good person, means so much more." Unless there's some unknown vendetta, the coach probably has some examples why he thinks that way.
Also, why run to the AD, to complain you received a bad recommendation? What is the outcome you're looking for? I can tell you of countless HS teammates of my son who went to our AD to complain about playing time, coach attitude, etc. Nothing will come of it. Ignoring the head coach, rather than trying to repair the situation may also not be the best thing to do.
If you address the situation properly, both with your son and the coach, you may find this is the best thing that happened to your son.