I can understand why the question was asked - where is the link between the broken and the rest of the list?
There is more to a sentence than syntax; it is also an act of communication. When we communicate, we usually believe we are making sense etc - the Co-operative Principle and all that. There is not much point in communicating otherwise. In this case, saying the alleged burglar had ribs and a jaw is hardly news, and unless the story is leaving out something very interesting he had them before he entered the house and nothing Mr LL Cool J did left him with them.
In short, the story makes sense, and succeeds as an act of communication, only if the nose, jaw, and ribs were all intact when the alleged burglar entered, but were broken when he left.