This is a popular low-traffic route for pedestrians and cyclists to access the Intercity commercial district and so it seems reasonable to try and separate this traffic from the off-leash dogs in the park.
However, on one occasion when I followed the directions on the sign, while walking through the park, I was joined by an aggressive dog who didn't read the sign. This dog's owner/master/human companion was on the other side of the fence. As the human became concerned and began to raise his voice while trying to call the dog, the dog perceived me as a greater threat. I was lucky that the dog didn't bite, but it did nip, bark and growl as I walked, as calmly as possible, to the end of the fence where the snarling beast was reunited with its human.
As I continued on my walk, it occurred to me that the dog owner and all of the other dog walkers are themselves "pedestrians." Why don't all the humans walk on that side of the fence. Because that would be ridiculous, right?!
If anyone asks why I now always walk on the "Dog" side of the fence (I still cycle on the other side during the summer) I am prepared to introduce them to my invisible (and possibly imaginary) dog, Harvey. If they get to walk on the "Dog" side of the fence then so do I. Otherwise all dogs should be required to pass a reading and comprehension test before entering the park.
The fact that people walk their dogs far past this fence along the old railway bed, means that every pedestrian and cyclist using this route must interact with the dogs anyway.