I think thats the reason why Banner was fired. Haslam was very interested in Schiano after Belichek called him twice personally to recommend him. I'd take Belichecks opinion over Banners.
I see your point, but I'm thinking that Haslam panicked because Quinn wasn't going to interview until after the Super Bowl and Pettine was going to back out if the Browns didn't make a decision. Also with the way the Whisenhunt interview went down that could have played a major factor into the panic. Guys were turning down a head coaching offer in the NFL with a team that has 3 picks in the top 35, and a great salary cap situation. Why would a potential head coach do that? I think that Banner was the reason.
My theory is that he hired Pettine in a panic then after he calmed down realized that Banner was a problem and axed him.
To clarify, this is what I think happened. I've made panic decisions before then had regrets soon after and had to deal with fixing the mistake.
I also think Haslam has bigger things to worry about. Like the Flying J fiasco.