More likely they tried to get into the throttle during the turn at the wrong place, or tried to brake during the turn when caught off-guard, both of which would upset the balance of the car and send you off the road.
Traction control (or intentional chassis/suspension design) might have saved them from oversteering (spinning out towards the road), but not been able to prevent them from going off the road
Turn-in is actually noticeably improved by lower tire tread on tires (as long as your tires are still roadworthy and the road is dry).
If you take a look at one of the most popular "sticky" tires for autocross, it almost looks like the tread has completely worn away on a normal tire: https://www.tirerack.com/images/videos/video_images_758x426/...
More likely they tried to get into the throttle during the turn at the wrong place, or tried to brake during the turn when caught off-guard, both of which would upset the balance of the car and send you off the road.
Traction control (or intentional chassis/suspension design) might have saved them from oversteering (spinning out towards the road), but not been able to prevent them from going off the road