A confusing picture about who remembered what about the crash was painted at the press conference at Bethlehem College yesterday.
Mr Crosbie said a small number of people had witnessed the change in driver.
"Because everybody was involved in this accident to a greater or lesser degree, it's taken time to put together the pieces so that we can in fact rely on the information that we are getting.
A Facebook post by Kerri Tilby Price, a teacher on the trip who was travelling in the car ahead of the minibus, confirmed there were confusing reports as to what happened because of some students having no memory of the accident at all, and some remembering only parts.
Meanwhile, the man who allegedly told Mr Fellows to keep quiet about being the driver denies he was involved in a cover-up.
Mr Crosbie said the school's Kenyan liaison representative, Calvine Ominde, told former student David Fellows to keep quiet about the driver swap until after the teen had returned to New Zealand.
However, Mr Ominde has denied being involved in a cover-up.
Mr Ominde told TV3's Firstline this morning that when he arrived at the crash scene Mr Fellows approached him and said, "It's my fault".
"I didn't know what he meant because I knew [Kenyan driver] Chris [Mmata] was driving," Mr Ominde said.
He said Mr Mmata's body was lying near the driver's side of the minivan and he had no knowledge of a driver swap before the crash.
Mr Mmata and New Zealanders Brian and Grace Johnston and Caitlin Dickson, 19, were killed when the van rolled into a ditch on the Nairobi-Murang'a highway nearly two weeks ago.
Mr Ominde said he did not know there had been a driver swap and he did not understand "why I'm being blamed" for a cover-up.
"I hear there's a lot of news saying that I covered up for this. Why should I cover up for this when I'm mourning the death of my friend?" Mr Ominde told Firstline.
Mr Crosbie revealed yesterday that Mr Fellows took responsibility for driving the minivan, which had been carrying 16 group members, when it crashed.
This morning he told Radio New Zealand there appeared to have been an initial cover-up.
"I think you talk about a cover up and this appears to be an initial cover-up but there was never an intention, I believe, for a long-term cover-up because David was told to tell his family and to tell the school," he said.
"There was mayhem, there was people dying, Calvine had to do what he had to do to help and get people to hospital."
He agreed that it sounded like an attempt to pervert the course of Kenyan justice.
"Yes it does, and those people were told by a man that they trusted and respected in a foreign country what to do.
"I can only surmise that in a situation like this where there's a man like Calvine who they highly respect telling them what to do, then you do it."
Mr Ominde told Firstline the school "should tell us the truth about what happened".
The school has launched a private investigation following the latest revelation.
School board chairman Greg Hollister-Jones told Radio New Zealand the intention of the investigation was "so that the truth is told and learnt".
"We are a community that puts truth at the centre, and we need to know the truth. The second focus is what learnings the school can make because it wants to continue these overseas trips.''
He expected the investigation to take several weeks.
Police here said they would forward new information to Kenyan authorities through Interpol.
Lawyer Gary Gotlieb said had it been made known to Kenyan authorities that the 18-year-old had been driving, he would possibly be in a Kenyan jail right now.
The teenager could still be charged, Mr Gotlieb said.
Read more: NZ police to tell Kenyan authorities of driver swap cover-up
- APNZ, NZ Herald, Bay of Plenty Times
