I haven't seen the video yet, but it's not difficult to make a real car into a remote controlled car. That one Bond film, with I think the 7 series was remote controlled off the set (albeit from inside the car) and the people on Top Gear have had a RC car race!
edit: yup, just saw the video, and that's the Top Gear episode I was thinking about. But they don't show the race where they race this RC car racing champion (who is a girl:Q)