Constable Tina Mitchell-Ellis told a coroner's court that the three who died and a fourth who suffered brain trauma in last May's accident weren't wearing belts and were thrown from the van. She said four others who were wearing belts suffered only minor injuries.
The students were in New Zealand on a study-abroad program and were driving to the start of a scenic hike.
Driver Stephen Houseman last year pleaded guilty to careless driving and was disqualified from driving for six months.
Mitchell-Ellis said Houseman had earlier reminded the others to buckle up. She said he became distracted and drove onto the side of the road before overcorrecting, flipping the van four times.
"As we were flipping, everyone was screaming but it was more like a rollercoaster scream," Housman said in a statement to police that was presented at the court hearing. "I just kept screaming 'I'm sorry. I'm sorry. I'm sorry.' I did not know what else to say."
Police said alcohol and drugs weren't involved and the debris indicated Houseman likely wasn't speeding on the rural road when he crashed. Police said it was his first time driving on New Zealand roads and his first time driving a minivan.
Those killed were Austin Brashears of California and Roch Jauberty of France, both aged 21; and 20-year-old Daniela Lekhno of New Jersey. Meg Theriault of Massachusetts suffered head injuries.
The Associated Press tracked Theriault's struggle to recover from the accident, as she returned home, underwent cranial surgery and returned to Boston University in January to audit an accounting class.