I think I'll come at this from a slightly different angle. I think it's a sad reflection on our society that you have enough fear to have to post this question! I'll bet every single one of us played over at the neighbor's house(s) as kids and most of us likely got hurt a couple times. Did our parents sue the neighbor? No! Why not? Because #1, they were our friends and no harm was intended. And #2, us kids probably incited the injury onto ourselves through no negligence of the neighbor.
If a child isn't taught how to play safely, how will they ever learn? Plus, how will they learn personal responsibility if things are never their own fault? I'll give an example: my boy was at daycare up through kindergarten. He decided one day to jump off the chair/couch there. Repeatedly. He was told to stop and he definitely isn't allowed to pull that stuff at home. He ended up losing his balance and breaking his arm. I most certainly did not sue the daycare center. It's not their fault that my kid did something dumb and ended up getting hurt. They warned him to stop and he didn't. That's entirely his fault. Yes, we were saddled with the medical bills, but that's the price we pay as parents and as teachers of responsibility to our children. Now, I didn't go about blaming him to his face, but rather, used it as a teaching moment that yes, there's a reason we grown-ups say "Stop!"
It's a whole other story if there's truly negligence (such as a rusty metal spike sticking out of a public area that the owners have been warned about and didn't do anything and then my kid trips on and impales himself--no that hasn't happened). But this is YOUR well-maintained swingset on your property. And it really seems like we, as a society, have forgotten what true negligence is.
I guess we should all have some liability waivers on hand just in case someone comes into our yard to play. Everyone must sign a form saying they will not sue and have it notarized before allowing our CHILDREN to play together.