That numerous religious Jews attended the funeral of the Druze policeman is admirable and understandable.  He lost his life while trying to defend Jews and attending his funeral expressed appreciation.

What I don't understand as readily is when people pay shiva calls when they have no personal connection to the mourners and don't have a life story that is similar so that they can say, "We went through that and you'll see, you will be able to survive this and move on."

I could have easily gone to pay a shiva call to the Kletzkys following the tragic, grisly murder of their little boy, but I passed their building and didn't go in.  I could not fathom why my presence, as a stranger, would provide any comfort to the mourners.  I understand the feeling that we are all brothers and sisters, that we are truly one, but I think we need to do what's best, most comforting, for the people involved. 

I've read touching accounts of strangers visiting injured soldiers in the hospital and in most cases, it sounds like they really appreciate it.  So that's a great mitzvah of bikur cholim.  But unless a person knows that mourners are happy with strangers visiting them, it might be a good idea to be wary about doing so.  The mitzvah is to console them, not to rack up mitzvah points at someone else's expense.