While Vandy's NeuroCare Unit is run by Anesthesia, an important distinction to make is that anesthesia is not the primary team on any patient (I did my Critical Care rotation on the unit there). So it's considered an open unit. Therefore, the neurosurgeons and neurologists make many of the decisions and there can be primary team/critical care team issues at times. Many of the units in academic centers that anesthesia is running are actually open units, so that surgeons of all types are acting as the primary docs, with anesthesia doing the procedures, call, emergent issues, etc.
Just thought that might help to answer the OP 🙂