Playing the devils advocate here: There was (apparently) no physical contact between the cars, so one could just tell a different story about the type of accident, or just leave out that the Camry then pinwheeled into the median. (Reason for lying about it could be that they drove the car in autonomous mode on 'forbidden routes' and feared repercussions).
Having said that - I doubt that's how things happened.
It doesn't sound like the cars collided. The original story [1] includes more details, but it definitely sounds like a collision was avoided, and that avoidance caused the spine injury and the Camry pinwheeling.
> The cars continued speeding down the freeway side by side. The Camry’s driver jerked his car onto the right shoulder. Then, apparently trying to avoid a guardrail, he veered to the left; the Camry pinwheeled across the freeway and into the median. Levandowski, who was acting as the safety driver, swerved hard to avoid colliding with the Camry, causing Taylor to injure his spine so severely that he eventually required multiple surgeries.
> The Prius regained control and turned a corner on the freeway, leaving the Camry behind.
That’s about as amazing as Hollywood accounting.