"[The driver] has been attending serious accidents for nearly 30 years, and on this occasion he has made a foolish mistake and unfortunately let us down."
Parks Towing general manager Stuart Gerring said a review into processing vehicles from serious crashes had "very much started".
"I'm not happy that it has happened; I think it was a really poor decision," he told Fairfax.
Acting Canterbury district road policing manager Senior Sergeant Kelly Larsen said police were keen to prevent a repeat of the incident. She had spoken to the manager of Parks and planned to meet with him.
"We need to look at whether that's best practice - I would say it was perhaps not."