That's what they have to decide.
They also need to decide exactly how they want to apply this philosophy as it pertains to future managers. I'm not a big believer in the autonomous manager model, but if you're going to have the head coach as 'just one head of a department' in Cortese's phrasing, they need to be that, always. This:
SFC is not an unfeeling corporate machine, and in times of goals aplenty and top eight places there is leeway on our methods, but given that most departments have voiced concerns over the direction and atmosphere of the first team, and those who are seemingly barred from joining it, adding to Koeman's unwillingness to commit and our horrific run of results (Information that has been passed on end)
...is entirely understandable, but it's also not difficult to see where it can cause things to break down. When things were going well, Koeman was given leeway to operate as he wished. When things took a turn for the worse, the board and other departments wanted a greater level of control over operations. You cannot structure an organization such that authority is given and taken away dependent on short-term results, or you're going to get power struggles.