I think it is almost entirely that cars are more safe nowadays than they used to be. And I expect it has less to do with "collision avoidance maneuvers", and more to do with better design and crumple zones, and a significant focus on crash test ratings. There are probably as many accidents as ever, it's just that less of them are fatal.
But my original question was (expanded for clarity): "Why was there a sharp drop from 2007 to 2009 after many years of very gradual decrease or even flatness? Your answer could explain a steady drop as safety features become more widespread, but that didn't happen from 1995 to 2005, even though presumably people bought new cars during this time.