Haroush, your right, it would depend on the situation. "is it a situation where it is not that important to be right?" Yes, like in petty family arguments where it is to work stuff out instead of winning arguments.
I know sometimes the wrong thing is right. Example: doing something illegal is right, in a case where you're driving a sick friend to hospital at 2:00am. You come to a red light and plow through it knowing that nobody else is coming. Nobody will say that was the wrong thing to do.