As I thought about this, I realized a distinction is made between crises that occur because of inadequate planning/execution (avoidable crises) and crises that occur mostly because of external, unexpected changes in circumstances (unavoidable crises).
Pulling from some real-life crises I've seen recently, an avoidable crisis would happen when you realize you forgot to file paperwork to get health insurance and your child is due to be born any minute. An unavoidable crisis would kick into gear when you get a phone call indicating your mother has had a stroke.
The response in either case is the same - DROP your lists, because the highest priority and the first action in this "project" becomes obvious. Call the insurance company, or go to the hospital to talk to mom and the doctors.
GTD becomes invaluable in both crises, but for different reasons:
Avoidable crises: Ideally, with GTD you should be able to see the lay of the land and prioritize well enough to prevent these entirely. In the real world, when you're not a mind-like-water black belt and an avoidable crisis occurs, GTD provides the framework to:
1. Have the materials you need organized enough to work through it more efficiently and faster.
2. Allow for you to pick up where you left off after the crisis is finished. Instead of the slightly-confused "now, where was I" feeling, you can simply pick up your next-action list and keep going.
3. Once you've come through the avoidable crisis, you have the tools to figure out how to prevent it next time - where did the gap occur here? Did you collect something but didn't process it correctly? Did you neglect to do weekly reviews until a project snuck up on you? Is there something that isn't getting checked that should be, and should therefore be included somewhere in your process? Do you need to create a project to maintain or periodically fix whatever it was that broke?
Unavoidable crises: Having your next actions documented allows you to completely focus on mom. The list will be there when you get back. Sometimes you can literally hand a context list or project folder to someone else to handle until you can recover from the crisis. Without GTD, that wouldn't be possible.
During any crisis, your ability to effectively process information goes down to zero. I disagree that the next action during a life crisis always obvious. When this happens, continue capturing. I've been there When a medical crisis occurs, all you can do is collect the myriad of instructions, requests, deadlines, notes, and handouts, and though it feels mundane, when you get home and collapse into a chair crying, at least those responsibilities are not swimming around in your head. They are waiting in a notebook for you to read, process, and do WHENEVER YOU'RE READY.
That's the key for GTD. It stops and starts, but as long as you're somehow using the workflow Allen prescribes, it is helpful. I know business crises feel different from personal ones, but the workflow is the same. Collect, process, organize, review, do. Do what you can, when you can.