We humans commonly call that "aggressive" when a dog tries to take a ball from another dog or when that dog defends his toy. I take a little different meaning from that behavior. A dog that takes a ball off another dog (who has possession of the ball) is a little naive about "proper doggie etiquite and food distribution. But organization and disribution only happens in pack animals and even then it's a somewhat limited or irregular an activity. A dog that takes a ball that has been thrown for the other dog, but not yet in possession of that other dog is not being rude in my opinion. Possession is 9/10ths of doggie law. It's normal behavior...two animals wanting the same resource. And fighting or lashing out at the other dog regardless of who stole what or who had it first is also normal behavior for a dog. It doesn't line up with our morals, but dogs are dogs are dogs.
Contrary to popular opinion, dogs are not pack animals, don't enjoy joining up with every dog they don't know in an interactive fashion.... and it is certainly unnatural for them to get along, share or distribute limited resources with a bunch of random dogs that they don't know well, don't live with, don't share a home with. There is no evolutionary reason why dogs should share resources. Animals don't survive very well in order to reproduce and evolve if they say, "Sure, go ahead and take my bone." (or ball/toy) If a dog thinks he stands a chance of getting something he wants with minimal risk, he may well try it, regardless of "politeness." It's an evolutionary, advantageous and adaptive behavior to try and get the resource or try to keep it...not an aggressive ("mean") behavior.
So.......that being said, I think if the park rules say to keep toys away...they have a legitimate request. This kind of "aggressive" behavior is not the fault of the owner who didn't "train" the dog to share and share alike as we humans teach our children. Management, keeping an especially reactive dog under control IS the responsibility of the owner. But off leash, that is very difficult. And those dogs need exercise too. So, I agree that toys and playing fetch can be done at home, somewhere else or when the park is not busy...where there are dogs who couldn't care less about the ball. And if a dog is truly aggressive, dangerous, going after other dogs and wanting to fight, then they really need to either be under control or not allowed unless they're the only dog in the park at the time...something like that.
I am certainly no authority on dogs parks. There are none close to me because I live in the mountains and there are all kinds of places to run off leash, even on my own land. But, I don't think, by the sound of it I would be a fan of dog parks.....generally speaking. I think I've only taken a dog to one one time when I was visiting elsewhere. Lyric got along fine with a Corgi and I think one other dog. It was not busy at all. He was a dog-reactive dog when on leash, but not truly aggressive and too, this was when he was younger and less that way. Plus, he couldn't care less about toys or balls. He just wanted (now get this) to play and to herd the Corgi when he ran around. My goodness, could that Doberman herd! And a Corgi no less. LOL.