There's a documentary about it.
I believe strongly in private property and think if you can use it to solve such a problem, you should. But not all problems can be solved that way. Regulation stopped the filling in of the Bay, which, if allowed to continue, would have been an enormous loss. It was certainly the only solution people could see at the time. And I can't envision an alternative that would work.
Other problems, like overfishing, can be solved with property. The right to harvest a particular population at a particular time (and that can be bought and sold) creates an incentive not to overfish.
But not all types of ownership make sense. A resource owned by many people, all competing to extract all they can before the other owners do is itself just like a tragedy of the commons. Water rights often work this way. Better for these folks to have shares in a corporation that owns the resource. Better for them and better for the long term use of the resource. Even public ownership would be better than a privately owned tragedy of the commons.
Private ownership and regulation are just different solutions to that same problem. So you can have a regulated amount of grazing (where in theory scientists decide what level the land can sustain), or you can privatize the land and force the grazer to absorb the loss in land value from his activities, thus internalizing the externality.
That out of the way, I don’t think the article is correct. History is replete with societies whose self-regulation mechanisms failed and resulted in environmental disaster.