[meric]

Apologising for mistakes that aren't your own can also be a sign of supplicating - saying anything to get on the other person's good graces. If the other person's in a confident and strong position often there's no need to apologise for things that are not your fault. If you're dancing with a very good dancer and you're a poor dancer, and she knew that to begin with, there's no need to apologise. Instead, own your poor dancing ability. Exaggerate a little your poor movements. Laugh. Often a person of high skill level don't want to play with a person of low skill level might not even be the skill difference but because they don't want to deal with the low skill level person's insecurities. 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.

[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.