First, he answered the question then he used a transition, which is a rhetorical device you see public speakers use to "get on message." The transition was "But again, more than anything."
You also have to look at the context of the message he transitioned to. Coach Dungy knew this message would be, to some extent, unwelcome.
The next rhetorical device Coach Dungy used is repetition. He concluded his statement with "And we're more proud of that." To stay on message you need to state the message ans then restate it.
The message is clear to me - Coach Dungy is more "proud" of his relationship with God than his accomplishment viewed in the context of his skin color.
Whatever...obviously you guys need this in your corner more than I need to argue the intent.