My professor was going over the nuances of "bad news" wording, and he explained the nuances between being sorry, apologizing, and regretting something:
He asked us to compare the following:
I'm sorry that your grandmother died: Correct
I apologize that your grandmother died: Not really, unless you killed her and feel bad about it
I regret that your grandmother died: Not unless you actually knew her
Comments
On a similar note...
Situations where certain insults would not work:
Person A: I can cook a good meal.
Person B: Your mom can cook a good meal.
Person A: Uh... yes, she can?
Person A: I have pimples.
Person B: Your face has pimples.
Person A: I just said that.