When is it appropriate for a customer to foot the bill for a mistake that wasn't theirs?
While the main objective of any business is ultimately to make money, pursuing a little extra profit at the expense of decency and standards is a surefire way to lose customers who feel like they deserve better treatment when they are already paying for a product or service. Just because a clientele can be difficult or annoying sometimes doesn't mean that the average person just trying to get something done should be treated with contempt.
As in all walks of life, honesty is the best policy if a business happens to mess up whatever it provides to its customers. While there might be some select situations where lies and audacity seem to do the trick, those who care about integrity are better off playing it safe. That is how you have a chance at retaining customer loyalty even if some things go wrong.
Unfortunately, there are plenty of unscrupulous people who do not care about these principles so long as they can make a quick buck. From the perspective of the customer, the best thing that can be done is to call them out and fight for what they are owed. This is not always going to come easily in these kinds of situations. When making money is more important than being fair, a business probably won't go down without a struggle. The question is whether it feels like it is going to be worth the effort.