Inspired by the famous question, something subtle about it struck me.
Harry definitely witnessed and dealt with Cedric's death. It took a while before he could see the Thestrals because it takes a while to process loss. Luna can see them because of her mother's death. I believe Hagrid can see them because of one or both of his parents' deaths.
Now, is there any evidence to say if Hagrid and Luna literally witnessed death (reasonably unusual but it happens - though Luna would have seen her mother's particularly unpleasant sounding death, poor girl) or does experiencing the loss and processing the passing count? In this case, most Hogwarts age students should probably be able to see the Thestrals assuming that the death of a grandparent or other relative would count.
So, do you need to witness death, or experience a loved one's passing?