Yes, I believe it was even in 2 videos. One I remember that it was just gameplay from different cars / scenes / cities, amongst them you saw this car drifting across the streets of LA. It was raining BTW.
And I don't know why but I have a video with Martin Edmondson in my head as well, where he's talking, and they show this car drifting in the rain. Maybe he was talking about another Driver game (maybe around the time DSF came out) and then he started talking about the roots and this clips were shown.
I just browsed the GameSpot pics and the picture of the real video are there.
There's some pictures which are "standalone", for example this one:
It's one of the press pics that everyone knows, and that is found everywhere. The pics before or after have no relation to it.
Then there's sometimes a succession of pictures with the same car, in the same location, that's the pictures that have been taken from a video. Like the beta yellow/black GSX in Miami, or this picture which was taken from the very very short TV ad for the game:
This one was on Driver-Dimension but the link to the video (which was hosted on another site) is dead sadly. I can't find this ad anymore either. I remember this huge flip, I never managed to do such a thing by just simply crashing into a car haha!