"The more you protest, the more guilty you look." That's the whole design of the argument - it tries to defer responsibility for a football product of a certain quality onto the "mission of BYU," the criticism of which is meant to make you look like a bad person; however, many feel that better on-field results are possible while simultaneously fulfilling the mission of BYU. The two need not be mutually exclusive and Bronco's statement here seems to imply they are.
Not saying this alone is a indictment of Bronco but I can see why it rubs people the wrong way (and I don't think it rubbing them the wrong way means they have character flaws).