The phrase, "The Customer is Always Right" is wrong. That isn't to say that you should tell the customer is wrong, but instead you need to focus on the customer's expectations. The customer's expectations are always what the customer's expectations are. Your job is to meet and exceed those expectations.
For instance, we have clients who have projector rentals shipped to their homes. Since it is a residential delivery, we can't be certain what time it will take place. Following the customer is always right mode is wrong. Because, well they might be wrong. Instead, if the customer's expectations are set early on, then everything will work out fine.
Some businesses fail to communicate clearly with the customer. We have fallen into this trap too. But, if you set the expectations correctly, then the customer will adjust to what is possible.
I can say (luckily) that our customers are very understanding when things go wrong. We try to set their expectations as close to reality as possible then go to every possible step to make sure those expectations are met.