[kibwen]

  > But if the other person is, for example, was the victim 
  > for a crime, then you might apologise even though you 
  > weren't the person who broke into their house.

Saying "I'm sorry" to someone that has suffered a tragedy isn't an example of offering an apology, it's an offering of sympathy. It's a bit strange that we overload the phrase in this way, but I can't imagine a situation where the distinction wouldn't be clear from context.

[meric]

It could apply if the person apologising is part of the police force, or if it's a family member of the perpetrator. I think it can be a little more than sympathy - a person is apologising on behalf of the society the person is a part of. A visitor to a crime ridden suburb is mugged. A passerby, feeling ashamed of his neighbors could apologise with a meaning more than sympathy. The scope of responsibility increases the less confident and less secure the receiver of the apology is. That's what I'm getting at.