The insult is usually connected with the injury in some way. It's as if someone has said, "I don't care that you've been hurt, even though my next action will make your situation worse."
Here are a few examples lifted straight from the net:
"Medical bills add insult to injury for Colorado shooting survivors..."
"Microbes, sponges, and worms -- the side effects of pollution and heavy fishing -- are adding insult to injury in Kenya's imperiled reef systems..."
"It's hard enough for employers to cope with hundreds of new regulations passed each year, added to the tens of thousands of regulations already on the books. But now, agencies are adding insult to injury by imposing standards that are impossible to meet."
"I think giving someone a ticket in a situation like this is just adding insult to injury." (comment about an accident victim then being fined by traffic police)