How do you retrain someone not to tell 2 planes they can use the same runway with repeated confirmations based on the fact that he thinks 3 miles is far enough away? At that point are we certain its not Alzheimer's?
A different regulation (applicable only to radar environments, which AUS is) allows for a departure if an arriving aircraft is 2+ miles away from the runway, as long as there is at least 3 miles of separation within 1 min after takeoff.
All that being said -- it is possible to execute a squeeze play like this if everything is perfect, but you need the departure to go IMMEDIATELY. Trying this in low visibility was extremely reckless and incompetent.