I don't know, I think generally people don't say sorry enough. You ask why say sorry if you don't mean it but in work I say sorry all the time, even if the issue is not my fault, anything to do with me, or is out of my hands. It just smooths things over.
It annoys me when dealing with companies that people just don't stick their hands up and say 'yes, sorry,' acknowledges a problem and go on to say how they will fix it. It doesn't have to be a big deal or dwelt on beyond that. 99% of the time all people want is an acknowledgement and if they get it they calm down. When I see threads on here about bad customer service, neighbour issues, etc. I do wonder how many of the issues could have been solved with just a simple 'I'm sorry about that.'
People seem to see it as some sort of huge admission of guilt or culpability or liability, or equate someone expecting an apology as wanting them to throw themselves on the floor and beg for their forgiveness.
e.g. in the example someone gave above about saying 'thanks for waiting for me,' rather than 'sorry I was late' to a meeting - well I think if you were late you should say sorry! By all means say thanks for waiting as well but if you've held up the meeting, you should apologise! But people instead whine on about 'it wasn't my fault, my first meeting ran late/there was bad traffic' - I don't care! Most of the time you could have done something to be here on time if you'd cared enough, and even if it was completely out of your hands, all you're saying is you're sorry about that, not admitting fault. If someone just waltzed in saying 'thanks for waiting,' I'd be a bit annoyed and would be thinking 'thanks for showing up/' or 'well we didn't exactly have much choice, cheeky cow.' Whereas with a 'sorry' I'd think 'fair enough, let's move on.'
I'm always impressed on here when people put their hands up and say 'Oh sorry, I didn't read the full thread,' or 'sorry I misunderstood,' when they've misread something or it's been explained to them. Happens pretty rarely though.
I do understand why over-apologising is an issue for women, and I try and remove the extraneous 'pre-emptive' apologies and general faffiness from my emails to make them more 'manly'/direct - all the 'hope this is okay,' 'sorry to bother you,' etc.
But generally I think saying sorry is a good thing, and people do it too little rather than too much!