SoCalKDG said:
What you want is "I am sorry, I screwed up, I'll do anything you want to make it better" i.e. in your business you gave them free laundry. While this is good, it doesn't tell you/them why the situation occured and doesn't tell you/them if the situation can occur again.
No, but what is does do is tell the customer that
no matter what the cause of the incident the business will come through for them.
Nordstroms - takes back shoes after wear if they are not to customer satisfaction. Disney will replace your ticket media if you lost it providing they can find the record of your purchase. Hollywood Video guarantees certain movies are in stock or they give you the movie rental for free. Thirty minute guarantees on pizza deliveries, comped drinks if your reservation for dinner is late, etc.. These are all things that companies do not
have to do, but when they do it gives the customer a level of confidence in them and a feeling of security. Customers don't usually switch loyalties unless there is a compelling reason - the big phrase where I used to work was "attract one customer today, attain their family for a lifetime".
As to the definition of apology, I think that the "defense" line is more directed at a formal defense of a topic. People are said to write apologies on topics. I found this:
Synonyms: apology, apologia, defense, justification
These nouns denote a statement that excuses or defends something, such as a past action or a policy: arguments that constituted an apology for capital punishment; published an apologia expounding her version of the events; a defense based on ignorance of the circumstances; an untenable justification for police brutality.
That isn't typically how we talk in everyday language, it is more lawyer/academic speak. Most of the time, what people want to hear is "I'm so sorry" not "I'm sorry, but..."