The chief should have disciplined the firefighter and/or relieved him of his duty. Looting is stealing and firefighters are trusted to go into people's homes. We can't have firefighters looting like that. I do not think that the needed to resign. He could have used the incident to set a precedent and make a point.
The Mountain Fire Chief resigned rather than impose a serious punishment on a firefighter. This firefighter abused the public trust by looting a FedEx truck. He only received a verbal reprimand. This sends the wrong message to the department and the city. The chief took the easy way out instead of doing the difficult, but correct, thing.
The firefighter's actions should not be a reflection on the Fire Chief. The Chief was not even present at the scene of the fire in question. The Chief certainly did not encourage the behavior of the firefighters the looted the FedEx truck. If the Chief had been present at the scene, or had participated in the looting, I would agree that he should resign from his position. However, I feel that the Chief stepping down in place of taking action against the firefighters that are responsible for the looting is a mistake.
We have this tedious tendency to demand a scapegoat for all things. Lines at the airport too long? Fire the head of the TSA. San Francisco PD officers making racist comments? Off with the chief's head! A firefighter loots a FedEx truck? That firefighter should be in prison, not his chief forced to resign.