Seemingly (IANAL) he could, in fact, do that. I think his concern would be if he's not properly maintaining it, now the beach near his house is going to fill up with trash, maybe overnight campers, etc. So he's either got to foot the bill to keep it looking nice, or end up with a garbage beach.
So it's definitely a sticky situation. Personally, I'd just open it up, I think people generally treat beaches OK in Cali, but I can imagine his concern.
As another commenter mentions, it seems like a very reasonable expectation that the state would maintain it.