I think the trailer is used to transport car dollies and things like that. If you look at the picture, the sides of the trailer consist of channels for the wheels of the dollies.
While this may be physically possible, I very much doubt it to be a safe practice if the trailer is loaded, or under less than optimum road conditions. The towing vehicle should be at least close to the weight of the towed unit, and the short wheelbase of the TDI would allow it to be pushed off track very quickly if the trailer developed any variation from a straight ahead motion, in direct line with the wheelbase of the car.
I'm thinking the highway patrol may have something to say to the driver, if they se this.