As I agree the terrain is rocky and steep, I have not heard of anyone getting hurt from the rope swings. Do swing at your own risk, but you are have a better chance of getting hurt by riding the MUNI.
Best Bad-Idea Swing - 2009
Billy Goat Hill Rope Swing
Billy Goat Hill in Noe Valley offers a lush, green field; great views; and quite possibly one of the most treacherous rope swings you should totally not try to swing on. The swing, which is routinely cut down by smarter citizens and then replaced by stupider ones, is strung from a tree that sits solo in the middle of the hill. No tires or wooden seats await those who seek out this plaything. Just tuck your foot in the hole at the bottom, grab on, and push off. Terra firma gives way to a steep incline littered with sharp rocks. Swingers who make it back to the ground intact will have enjoyed a fantastic view and the thrill all daredevils feel after once again cheating fate. Those who don't should tuck, roll, and pray to the deity of their choice. It makes the Seward Street Slides look like, well, child's play.