Whenever there is a critical incident there is always a debriefing or After Action Review (AAR) to follow. Generally, these meetings take place after the dust has settled from the incident and it gives all parties directly involved the ability to reflect on the incident and/or the response. As you might imagine tensions are high and people are overworked by this stage. For these reasons, it can be of value to have an outside resource facilitating the meeting.
A person coming in from the outside to facilitate shows neutrality. I have first-hand experience in witnessing the power struggles that take place during critical incidents and having a facilitator from the outside is imperative. Choosing to have someone facilitate a meeting such as this is crucial in order to keep emotions in balance while also effectively navigating the intended agenda.