I'd imagine that particular car had dual controls, and the journey was not only a carefully planned route, but a carefully planned time of day (i.e. nowhere near rush hour!). You can bet that by the time these become a reality they will have to endure testing far tougher than even the toughest driving test in the world.
Of course, unlike human drivers, they will follow the Highway Code to the letter. I doubt they'd upload their data but the onboard computer would probably have a running log of several hours worth of data readings from the video camera, sensors and radar so in the event of an accident, the data could be interpreted to reconstruct exactly what happened at the time of the accident.
Heck, I'd imagine insurance companies would give hefty discounts to users of these cars as once they've been approved for road use, they'd probably be safer than a human driven car and would make the claims process significantly shorter. However, it would have to be a factory fit, wouldn't be allowed to be retrofitted, would have to undergo renewed certification for every make / model / trim / engine size of car, and would add a very hefty premium to the car's price. There would also have to be a manual override for if you drove it under a low bridge and sliced off the radar, for racing and other unconventional activities - although no doubt if the system was functional (as opposed to damaged) the sensors would still operate so allowing it to prove whether it was the human driver or other factors responsible for any accidents!