I know, I know, shocking right? The people who know a lot less about a company/store than the employees that work there, are not the ones in the right all the time! Wow!
I have seen time and time again, customers talk their way into a promo or free product, just because the boss goes by 'the customer is always right.' I am the first to admit that I will always believe the best in someone because there is kindness somewhere (even if deep, deep, deep down) in everyone, but watching those customers do what they did, there are some people out there (very few but still some) that will do whatever it takes to get free or cheaper product.
Now obviously you need to be smart about this because if it deals with a product not being up to par, and you can physically see that, you need to fix it or deal with a refund; but when it comes to a customer talking about one of your employee's character, you need to ask questions first and then take it into action. If you know your employee to be outstanding and hard-working, with a great attitude/customer service rep, than most likely the man or woman talking down about them are manipulating you. Yes employees have bad days and need to keep it out of the workplace, but if something like that arises, talk to them first. See where they are at, why they think the customer is saying those things, and if need be, stand up for them!
Don't be a coward. Nobody wants to work for/volunteer for/intern for someone who doesn't take them and their character into account before going with the accusations.
There were two points that I once read on the Forbes website (yes I read Forbes, but no it doesn't always stay in my brain but this did).
1. Unreasonable customers eat away at your finite resources.
Most likely if someone is taking the time to complain, they will do it again, and every time they do they have all the time in the world. You as a business owner do not need to be using up all of your time trying to make one customer happy; if they are never happy with your suggestion, move on. Spend that time teaching your employees good work skills that will help them and your business flourish. Also focus time on your steady good customers. They don't complain because they understand how you do business, and they will respect you for it if you stick to your values.
2. This 'customer is always right' mindset places the employees against customers and management.
This should never be the case. Your employees need to know they work somewhere where they are trusted, respected, and that they are not just pawns to be thrown away when the time comes. Your employees will come to resent you if they think you will always choose a customer over them.
And my final thought on this is- just remember that that customer is a small, replaceable part of your company that when they leave, more will come; but your employee works there because they believe in the vision, and they are a lot harder to replace.