What world do you live in? Shit happens and people doing business between each other will mess up from time to time. Best thing is to think about how you would want to be treated if you were on the other end of the deal.
A situation where you did work for someone and everything you did was great and went together like you wanted it to, you might even be so impressed by your work you give the customer a lifetime warranty (like snap-on). But you mess up the billing and you don't get paid for that job, so you tell the customer about it and he tells you to shove it. Would you feel his actions were justifiable and would you honor the warranty you gave him?
If you find you have paid them already, tell them and take it from there.