This is the second story I've read in as many weeks where getting doored ended in death by way of the biker being run over by following traffic.
Barring avoidance of the accident, it seems like the biggest threat is not impacting the door, but falling into traffic.
They say (and I've experienced) that time slows down for the participants in these situations. (It's a function of our physiology that responds to high stress situations). It is certainly feasible that a cyclist would have more "time to think" about what to do than a stopwatch would seem to indicate.
Our first instinct might be to avoid the door, but does that impart a deadly vector to our body before it goes airborne? Better to stay straight unless you are already certain (based on your continuous situational awareness cross-check) that there is no overtaking traffic. It seems to me that if I ran straight into the door, the worst thing that would happen is I go head-first over the top of it along the same straight-ahead vector, and that if I'm able to maintain my wits, I can control my landing to minimize the force of impact and control which way I go after that. Just wishful thinking, on my part, but it would be nice if this could be tested, and perhaps trained. I suppose hardcore trial-bikers (and acrobats) would have a leg up on this kind of skill.
Of course, better to ride carefully and avoid being in the door zone, but I'm sure that's not always possible. Where I ride the traffic is light and parked cars are few. I don't know how I'd do in a heavy urban zone.