They work together. True leaders lead by example, which are outward expressions of inward beliefs. They are intricately tied. IMHO, perception is very important as a leader, especially to the young who look to such a leader for guidance. This also includes what comes from the mouth, which completes the understanding of the perception and sin or absence thereof.
I agree that perception is important. But because the school decided to act the way they did, we now know that the school was ok with hiring a divorced woman, but fired her for getting pregnant before getting re-married. And now the school will have to deal with the perception of hypocrisy because of it. By their actions, they have brought more scrutiny upon themselves.
BTW, I like your tagline.