I've always taken "The customer is always right" to mean that you don't actively confront and correct a customer even when they're wrong, because that's likely to upset them and maybe cost you a sale. It's not meant to be literally true. It just means that when the customer is wrong, you either skirt the issue or find a diplomatic way of handling it without actually saying they're wrong.
And that if it's over an issue that's not going to make or break you, it's worth occasionally taking a hit and helping the customer if it seems like an honest mistake on their part. Lose a little money here and there, but you more than make it up by keeping loyal, happy customers. Obviously don't run yourself into the ground, but if you are a little more lenient rather than nickeling and diming the customer, they'll be back again and again, and tell others how great you are.
LL Bean is a great example of a company like that. Their return policy is, in a word, stupid. They'll take back anything they ever sold, no questions asked, will fix it for you, give you a new one, or give you back what you originally paid for it. You'd think that would crush a company, but people will spend more money there knowing they stand behind their things, and the stuff is usually good enough quality that you never return it anyway. A few people will return boots that are 20 years old and worn down, and they'll take them, but most people won't ever use the policy, but just buy another pair after time. Doesn't hurt their bottom line to be on the customers' side, and probably helps them more than anything. Tell me how you feel walking out of a place like that rather than somewhere where you obviously bought a defective item, but it was 31 days ago, or lost the receipt, or you can't 100% prove it was broken right away, or whatever. You recommend the first place to everyone looking for that item, and you tell everyone that the 2nd place sucks, you hate them.