I worked at the Inglewood Bird Sanctuary as a university student in one of the children's programs they used to run there. Obviously, I asked about fishing one day and one of the head operators mentioned that there is nothing they can do to prevent people from fishing the river there, but that they will not allow people to park there and access it through the sanctuary.
IMO, this is for good reason. Once you open it up to fishermen, then why not other users? Why not bring your dog for a walk there, or launch your dingy. I guess the point I'm trying to make is that they would prefer to keep the place quiet and allow for proper wildlife viewing. It isn't just a bunch of birds, there are some pretty cool creatures all over the place if you know where to look. These people are not the enemy - so lets cut them a break. Fishing around there is poor anyway, as the above post mentions.