One thing to consider is what type of event will be a trigger for you to activate your EOC? A typical fatality accident is not something that would do it for most jurisdictions. Does it take a mass casualty event to be declared -- to activate? Would intense national media scrutiny in itself be enough to cause you to activate your EOC?
In the case of the incident above, the issue of international students being killed was a factor in how the Seattle EOC responded. Imagine the coordination required with both the fatalities involved and the other injuries, and parents and loved ones being continents away and wanting to get to their children as quickly as possible.
I don't have the details, but I'm betting the U.S. State Department had to be involved somehow. Passports, visas and all that those things entail. Housing assistance for people traveling to the region, etc.
Once the rescues are completed on scene, the incident is not over. It can continue for many days as people and agencies not normally associated with an EOC become involved in the human response to the tragedy.
You can't anticipate every event, but you can establish a philosophy about when, how and under what conditions the EOC becomes involved in circumstances that go beyond the "typical" emergency or disaster situation.