I have seen DBW cars throw in the towel when you decelerate and then reaccelerate. They take a bit of time to register your demands.
It might also be that it was changing down when you pushed down on the pedal, and the RPM didn't rise enough to give you any go, it's only when the gearbox downshifted and you had enough revs that it started to move. Also, I think during downshifts, it'll cut power to save the gearbox. Add all of these together and you've got a delay of a second or so between you pushing on the gas and the car responding - which is an infinity when you've got another car bearing down on you.
You haven't tried a small highly turbo-charged diesel engine in a heavy car I think. It'll give you an appreciation of the word "lag". I had an Opel Zafira for a weekend in June and pulling out of junctions was a lesson in throttle and clutch control. You needed to have enough revs to keep the engine from stalling, but not enough to burn the clutch. Added to that, as soon as the turbo caught up, you had to ease off the accelerator, or it would go like a shot to its redline. Power was available between 2000 and 4000 RPM. It was as slow as a pig below, and lag was astronomical. Still, was good fun revving it to 5K in each gear :D. Even so, it gave better than 14 kms/litre.
