As one well-acquainted with the Dornier 328, I may be of some assistance. Steering in the 328 is done by a tiller on the captain's side. There is a space about big enough for a standard aircrew flight bag immediately outboard of each pilot's seat, and sometimes crew keep a heavy book of approach plates on top of their bag. If that book went forwards at high speed as it did in this case it could either hit the captain's arm and make him make a rapid jerk on the tiller or even hit the tiller itself if the captain's arm is on the steering yoke. Either situation could result in an undesireable and rapid steering action at high speed.
This is not a design error but merely a feature of the system. The answer is not to stamp on the brakes! The slight difficulty in this situation is that ScotAirways may have gone to considerable length to downplay the significance of what has happened. Therefore the AAIB may not have been informed despite a minor injury to a passenger and the necessary checks done on the undercarriage despite the aircraft leaving the runway and ending up on the grass. I understand the aircraft was back in operation almost immediately as the entry in the tech log did not reflect what actually happened.
No doubt one day somebody will start digging deep and finding out the real nature of the operation and when they do 'there may be trouble ahead'! I do not think there is a genuine desire to have unsafe practices, but there is a total lack of grasp as to what the minimum standards of flight safety are in a modern Western airline.