The words we say when trying to comfort others can often be misunderstood or over-analyzed.
When I was in kindergarten, my friend Alex was knocked over, along with his block tower, by another student who was haplessly running through the area. When I felt bad or was hurt, my parents often said 'I'm sorry', and that was what I said to Alex when he got up crying. Alex wasn't comforted by my words though, instead he sounded surprised and angry. "You didn't do it! What are you sorry about?"
This is not just a child's reaction. In mortuary school, another fellow student and apprentice funeral director had been out to some one's home after a death. He told the widow that he was sorry about her husband, and her response was quite similar to Alex's, "What are you sorry about? You didn't even know him!" She was angry and felt that his comment was not genuine; just another line handed out to everyone without thought or sincerity.
Just as I didn't know how to respond to Alex, the apprentice didn't know what to say back to the widow, other than that he was sorry, and that hadn't worked very well the first time.
Unfortunately, the apprentice vowed that he wouldn't ever say he was sorry to a grieving person again. I hope that by now, he has changed his mind, because I know that what he was really trying to communicate was that as just another person, whether he knew the deceased or the family or not, he was sorry that such a sad thing had happened to her. Surely humans have not grown so callous that they cannot feel for strangers in their grief. In saying "I'm sorry for your loss" or 'I'm sorry about your mom" we are expressing our sadness about the situation and it's effect on another person, not pity or guilt, and not a claim that we know the depth or the unique personal feelings involved in this loss.
In a language filled with expressions that are not always meant literally; in which 'How do you do?' is not a question at all, but means 'Nice to meet you'; and the response is 'How do you do?' again, meaning 'Nice to meet you too', perhaps 'I'm sorry for your loss' may be the closest our words can approach the meaning that underlies them.
There will always be anger and misunderstandings where language is concerned, but I believe that when delivered with the correct tone, even a statement like 'How are you' will be understood by a hurting person to be an expression of caring and interest, and not the unthinking blunder that it otherwise could be taken for.
We need to continually be conscious and careful about the words we use with the grieving, but we should never stop telling them that we are sorry, that we care, and that we feel for them in their loss.