I think there are probably parallels to when Ferguson and Gill both left Man Utd at the same time too.
In hindsight, having both a new manager and a Director of Football, both with little experience of conducting transfers, was a disaster waiting to happen. As @Rhys suggested the other day, with a more experienced DoF the dynamic might have been a lot more successful.
Even a vastly experienced DoF starting a new job at the same time as a new manager with Koeman's strong personality would have caused issues. It was just unfortunate timing as they both will have wanted to establish their own power base at the same time. Should have been half-expected really, especially with Moshiri's comment of 'Koeman is Koeman, he does what he wants and I support him.' Starstruck much!