I believe "sorry" is used to express both of your apology and your sadness/regret/disappointment. How can you tell the difference in conversation?
For example if somebody said "I'm sorry the computer didn't work" to you, I would get confused about whether he apologized (=he meant it was his fault that the computer didn't work) or he just mentioned it as his opinion(=he just felt sad about the fact. he doesn't have intention to apologize).
I know it depends on context, but if you have some ideas to tell the difference, please share with me.

It's just a politeness thing to apologize for someone else's misfortune. Some English speakers have trouble with this, too. Sometimes I will say something like "I'm sorry you're not feeling well", and they will say as a joke "Sorry for what? It's not your fault!"

In general, people don't apologize unless it's clear to the other person that they did something wrong. So if someone said "I am sorry that the computer isn't working" and they did not say that they were responsible, then you can assume they were being polite and expressing sympathy. If they were apologizing, they would probably say "I'm sorry, it was me that broke the computer" or "I'm sorry, that was my fault."