The internet isn't exempted. You're just looking at the wrong party for liability. The people who actually put up those live streams are liable, and abusing facebook's service.
Same as TV and newspapers; you don't sue Comcast or the guy who installed your satellite dish, you sue the TV station; You don't sue the paper boy, you sue the news paper.
Same as TV and newspapers; you don't sue Comcast or the guy who installed your satellite dish, you sue the TV station; You don't sue the paper boy, you sue the news paper.