However, being right doesn't always mean winning the game. Sometimes, even if you know you are right, you have to let go and say, "my bad", "I'm sorry", "it's a misunderstanding".
It's always important to think ahead and evaluate if being right is worth loosing a customer, a business partner, a colleague or any kind of fruitful relationships you worked hard to establish.
Business relationships are like any other relationships, to make them strong and long lasting, you have to make compromises from time to time. Because, at the end, what' s the point of being right if no one is on your side?