To the OP: I am sorry your child had an accident, hope he is doing much better.
If one falls due to natural causes, rain, clumsy, etc, I absolutely to do not think one is entitled to compensation I don't care where it happens.
If the walkway was defective, that would be different. But things get slick in the rain.
I agree the OP is not entitled to compensation. Accidents happen. This past Dec I was at WDW, but went over to Universal early one morning in time for opening. It had rained during the night, but had stopped. I was in among the masses rushing to the World of Harry Potter and took the Suess Land shortcut like everybody else. Just as you turn off the main walkway into Suess Land the pavement changes. Just as I turned and stepped off into Suess Land I heard someone yell my name. My name is not all that common, so I instinctively turned to look back. As soon as I did, even though I was not walking fast and thought I was being very careful on the wet pavement, my feet flew out from under me and I landed hard on my butt and palms of my hands. CMs flew out of the woodwork to check on me. I got up and insisted that other than being embarrassed I was fine. They offered to take me to first aid, but I insisted I was fine and started to walk off. I hadn't taken a few steps before I heard a yell, turned, and found another lady had fallen in the exact same spot I had. I turned to make sure she was OK and her husband who was laughing, pointed at me and said "Didn't you just see her fall". The lady said she had and was being careful, but slipped anyway. The same CMs that helped me were helping her. We got to looking close at the pavement and noticed that about a footstep away from where the pavement changed there was a dip. Apparently both our feet hit that same little spot and with the water in it, it was enough to slip both of us. We both laughed, said we were OK and went on toward Harry Potter World. Just before I got back there, I noticed my hands were really hurting, looked down and found my entire left thumb, 1/2 my palm, and the first two fingers up to the first joint were swelling and turning black and the entire thumb on my right hand was also swelling and turning black. I round up with a fractured left thumb. I didn't even think of sueing. It was simply an accident.
Back when my eldest son was in elementary school, he and some friends decided to take a shortcut from the cafeteria through the elementary playground to the gym. It had been raining. the boys took a second to swing across some monkey bars and my son missed, hitting the opposite side, with his arm slipping off the wet bars, and he broke his left arm. Less than two months later my younger son was on those same monkey bars, slipped, fell to the ground, and broke two bones in his foot, a few months later that same younger son jumped from one side of those monkey bar to the other, missed, slammed his arm into the opposite side bars, and like his elder brother broke his arm. Since that was three accidents that I personally knew of within the same school year on the same set of monkey bars, I called the school to complain after the third incident. Guess what: my grandson now plays on that same set of monkey bars 22 years later. The school said it was an accident and accidents happen.