They did the math correctly, it was just different math than what they were supposed to be using.

The incorrect ratings were intentional and designed to look like they were correct so that no one would find out. It's easier to make sure no one finds out the number is wrong if you know what the correct number is and how to tweak factors here and there to influence it.

This was an incentives issue. They were paid by the companies they rate. So in order to not lose market share they had to certify junk.