Well you said a large reason. Which, granted didn't make sense, but I think you meant that most of the reasoning behind their departure was that they had picked up Bullard's way of life/way of acting, which simply wasn't true.
Tom Cairney leaving was the pivotal moment and key factor in our rise IMO. If he'd have stayed I doubt we'd have reached the FA cup semi never mind the final and Europe. I don't think we'd have stayed up last season either.