Here in Redondo Beach, and I thought Santa Monica was part of the LA County Beaches and Harbors, it is illegal to train for profit on a public beach. Beach use for profit or business is regulated through the city recreation and community services department. Just as you cannot get married on the beach without a permit, hold regular gatherings without a permit, have a dog on the beach, or smoke at the beach.
Seems to me that this protects the city and the community from businesses or groups who stretch personal boundaries. The beach is no longer a peaceful place for the strolling citizen when people are playing drums, shouting boot camp commands, or taking up limited space for their own business gain. If it is creating attention, then chances are it is annoying many people.