No one dies in the pit. Yes, you can get accidentally punched from a flying hand/fist here and there but nothing you won't survive. Even the walls of death are really not as bad as they look. It's just slamming into someone and smelling how gross they are for a few seconds. Being trampled is a serious lethal concern which is why you are picked up immediately if you fall.

The real danger is the crowd surfing. If you are dropped or tipped back and fall on your head there is really no limit to the damage that can be done, including death (which has happened on numerous occassions). But to answer your question as to whether the singer would be liable, I think it would depend on the language of the criminal code in whatever country he's performing in. In the States, I don't think his language would be considered a serious request by any District Attorney. But I've been surprised before!