On a sparkling Monday in June, the first session of the Flying Point Summer School surf camp was about to begin, and the beachfront parking lot was filled with cars: scrappy vans and pickup trucks belonging to the camp’s instructors, side by side with luxury sedans and a Maserati left by the mothers and nannies dropping the campers off. Out on the waves, the students, their hair slick with saltwater, were wearing new wet suits and lying across surfboards provided by the school. Ranging in age from 7 to 17, the students spend their summers in the Hamptons, in estates behind 12-foot privet hedges on pastoral lanes. As they paddled, the students were being pushed by the instructors, beach bums who had grown up nearby, the sons and daughters of carpenters and shop owners who cater to the summer trade. At noon the lessons ended...