Of course there are completely out of your control things like car accidents. Rape? Well that is totally relative. If it's as random as a car accident (i.e. rapist is hiding behind a wall and says "I'm gonna rape next person that walks by") then yes. But in many cases, no.
And illness, I'm half and half on this. I'm sure there are a group of islanders somewhere who have never seen a sneeze or cough and don't even know what one is, so they never sneeze or cough. (sort of like a story I read recently about how Darwin believed there were some islanders he passed when sailing who did not see his ship b/c they had no concept of what a ship was so they couldn't even comprehend it). Also, I see a TON of people who get sick (not talking cancer here) and it's very clear that it's a physical manifestation of their current state of emotions.