As the story gets added to, and now the child might have been hit (I assume, which might be wrong, not a spanking type of hit) then perhaps just being yelled at, my opinion might be different. To get the police there sooner, it must have been a lot more than a spanking, or at least the first person who called them must have indicated that.
For myself, since (at least in my city) yelling at your child does not indicate in the police eyes that physical violence is taking place, as I said, I would not have called, and I doubt the police would have come if I told them a child was being yelled at in the park (or even cursed at). If they did come, because (as you now said in your update) they thought there was violence, the child would not have gone home with someone who allowed abuse to take place. The child protective services would have been called immediately, so maybe you'll find out that the child didn't go home, but CPS took him instead.
I do believe it is considered different when you yell and curse at the police, than a child from your family. It's good as you have now found out from the other person that called that she called the police because she saw the child being hit. For me the difference was that you called because you saw the child being yelled at (cursed at), and you asked in the original post, under those circumstances, what would we do. I would not have called the cops. Since someone saw the child actually being hit, that's now a different scenerio, IMO.
But not always. I would say prob not even often. Lots of parents yell at their kids, and yet don't physically abuse them.