Well, I don't know how they do it, but there are a lot of access points between the beach and boardwalk, with hundreds of people coming and going between them. So I doubt it, but call and ask, I guess. The fee may just refer to parking access closer to the boardwalk, but like I said, I just parked on a residential street a few blocks away and walked (no parking meters).
Another activity suggestion that your son would probably like: I bought a boogie board and learned to body surf while I was there; it was lots of fun! I just got a cheap styrofoam one from one of the area's surf shops; I think it was around $20. There will probably be places selling them along the boardwalk.