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You're missing the point of the problem addressed by the article, which is not "whose fault it is?" but rather: "how come do we come to a halt when there is no actual obstacle that makes someone ahead of you stop?". The answer given by the article is that rapid deceleration propagates backward and intensifies, until someone has to stop even if the car ahead of him had not stopped.
The novel idea is in the end the fact that if you break late, by a matter of imprecision in adjusting your final speed after breaking, you are forced to slow down to a speed which is _less_ than the speed of the car in front of you that made you break.