Men and women say 'sorry' for different reasons.
Men generally apologise as an admission that they made a mistake or did something wrong. They apologise less frequently than women because it's so personal.
Don't make the mistake of thinking that women say sorry for the same reason. A woman says sorry so that you can put it away and move on. She's not necessarily saying she was at fault.
The distinction can cause confusion - at work as well as at home. Do we say sorry or not? Are we building a bridge or admitting an error?
Acknowledging the other person's feelings
How about this? Let's agree that an acknowledgement of the other person's feelings is always appropriate when they are upset.
First, think about the situation from your colleagues' perspective - how aggrieved are they? Would an acknowledgement of their feelings and the situation be enough to help them let go of their anger?
Try a 'run-of-the-mill' acknowledgement such as 'I appreciate this is terribly upsetting for you' but if it isn't enough for the person to feel as though their grief is heard, you may need a stronger acknowledgement, one that includes 'sorry'. "I'm so sorry that this has happened. I can appreciate that it is terribly upsetting for you" gives more value.
Getting the level of acknowledgement right
The golden rule is that the level of acknowledgement (including the potential for apology) should match the level of the grief experienced by the other party. If you are worried about liability, there are two 'if' apologies you can use that allow you to help your client without hurting your cause.
Try one of these when your expressions of concern aren't cutting it. "I'm very sorry Mr Jones, if this has been your experience of us, I can absolutely see why you are upset" or "I'm sorry Mr Smith, I can appreciate your situation, if this had happened to me, I'd be angry too'.
Whether you choose acknowledgement or apology, remember to match the level of grief the other person feels, but don't overdo it.
Under-doing it won't work for you either. People will go to court to get the equivalent of an apology - a judgment that recognises they felt aggrieved, so step up and say sorry when it's warranted.
Remember 'sorry' can be a high-end acknowledgment without accepting blame.