First of all I have no doubt on Wilcox's knowledge on football, definitely better than good old Woodward. But knowledge is 1 thing, responsibility is another. Let's take the other Football Operation Director as example, who's job is to look after the Stadium and pitch. All the shit inside the stadium is his (or her?) responsibility, but not the shit on the pitch. If someone step out of his JD and start pointing fingers at everybody's performance (except his own of course), you are asking for trouble.
During the summer recruitment planning meeting (or more likely in May), all senior staff can raise question on playing style, which lead to requirement of type of players, hence recruitment strategy and Academy training plan. But this is long term planning, and if the manager has the support of the Board, you have to support his style. You certainly have no right to leak to the press and try to influence tactics ( I am not saying Wilcox did that, but someone did)
BTW, we do have plenty of directors, but none is responsible for football performance.