Inspector Steve Mastrovich said the car "smacked head-on into the truck and trailer".
Any prudent driver would not have overtaken another vehicle along that section of road, he said.
Mr Blake has a broken left leg, two broken bones in his left forearm, two broken ribs and grazes on his body.
In the statement, written in Spanish, Mr Blake said he felt "fully gratified to be able to enjoy a great peace" while living in a town in National Park.
Mr Blake said he remembered talking about the game and then "a giant light dazzling our eyes".
"After a long silence (for me), I began to hear the loud sound of a helicopter and a lot of screaming people about to organise something, in my vision I can't remember much, I couldn't see or feel my body.
"I woke up after a few hours in bed, four people looking at me and asking questions, which I couldn't understand much. Gradually they starting telling me what happened, and still found it hard to understand.
"After a few hours my girlfriend Macarena came to the room, hugged me and we cried. She explained what had happened and that my four fiends had died.
"Many doctors have checked on me. I have had surgery in my abdomen and multiple fractures. I still have difficulties to move, but I am improving rapidly thanks to the care received in the hospital.
"I am very grateful to the doctors, so many nurses, physiotherapists, occupational therapist, dietitian and all of those who have eased my pain and are making my recovery possible.
"I hope to return to my home in Chile soon, but I will never forget what this country and Waikato Hospital have done for me."
Waikato Hospital trauma director, Grant Christey, said Mr Blake has come through all his surgery and is recovering well.
"Hopefully he'll be heading home in the next few weeks. He's made fantastic progress.
Dr Christey said Mr Blake's recollection of events was understandably poor but he was "extremely fit" which has likely helped with his recovery.
"I'm sure this has made a big difference, he has recovered very quickly from a serious set of injuries.
"He's lucky not to have suffered a brain injury and should have a reasonable recovery."
Dr Christey said Mr Blake was now freely conversing with family members in his ward and to his friends in Chile via email.
"He's got a very supportive family who have been by his side. Obviously he's got a lot to deal with but I think he's coping well," said Mr Christey.
- Additional reporting by James Ihaka of the NZ Herald
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