It sounds like your son has a lot of options for off-season training. What a great situation to be in!! If he has access to a swimming pool, what a great resource to use in the off-season. Imagine the resistance training he can perform with the overhead arm rotations. Plus, the constant resistance training with the lower body, coupling in the explosive moments in the wall turns. He will definetely get good training of the decelerators in the shoulder and upper arm, along with the lower body. But, it sounds like there is a conflict between you and a person at school. I am sure you can reach a happy medium with all the tools that your school has to offer. Each program and coach will have a different way to train their players. The question becomes is the methods getting results? Are pitchers throwing harder? Are position players getting quicker? Is the team bat speed getting faster? If the answer is yes, than I think you don't have to worry about your son because the school is doing the right thing. If pitchers are constantly getting hurt and your team can't steal a base or hit a double, you may want to start asking some serious questions.
If you are that worried about your son's training, I would suggest a winter sport. What about swimming or wrestling? Both sports promote great overall body strength and endurance. It sounds like your son is quite an athlete so he would be helping out other athletic programs in your school. Playing multiple sports provide the best training of all because of the 5 day a week practice schedule. What a great way to get ready for the upcoming season!!