I couldn't imagine a HC having enough time to become familiar enough with teams outside of their own conference to fill out a Top 25 ballot. Seems like the HC would just tell somebody in the AD to fill one out for them. I'd like to think Mullen doesn't watch enough TV or read the internet enough to be able to evaluate Missouri vs. Oklahoma State, etc.
I don't remember what year or what the occasion was but I remember Spurrier was questioned about one of his ballets and he said he didn't fill anything out. He gave it to someone in the AD department (like you stated) and they filled it out for him.