I don't know exactly. He was going to leave at some point, post-Brees retirement. I think most Saints fans at SR.com realize he wasnt going to be here for a messy, perhaps unsuccessful rebuild. Thats understandable and I can live with that, the NFL is a business, first and foremost. He could've just left with a little more class and not given some Saints fans and reporters the sense or notion that he was glad to be leaving and couldn't wait to coach somewhere else soon. Like coaching the Saints had become this "massive burden" he couldn't longer handle and it was a relief to be free again.
That sort of exit does run some people the wrong way even if its unintentional.
But, you're also right, in a certain sense. What would or could have been the right way for Payton to say goodbye and move on to his next coaching challenge?