Bethlehem College last week admitted he was driving the minibus, not Kenyan driver Christopher Mmata, when it crashed, killing four people.
Kenya's Traffic Act requires drivers of minibuses - known as "matatus" - to be at least 24 years old and to have held a licence for cars or commercial vehicles for four years or more. A matatu is defined as a public service vehicle having seating for up to 25 passengers.
Traffic laws were the subject of a major publicity campaign in Kenya while the college group were there. Kenya Broadcasting Corporation deputy editor-in-chief Samuel Maina said Kenya's Ministry of Transport launched "a huge campaign" around mid-November.
"The issue of road carnage is a big issue in Kenya," Mr Maina said.
When asked whether the fact Mr Fellows may have been driving illegally would make the group's travel insurance void, Mr Hollister-Jones said: "This was still an accident and insurance is to cover accidents.
"I have no comment on whether or not it was legal for David to drive. That's one of the things that the board of trustees' investigation will be looking at," he said.
Mr Hollister-Jones said he had "no idea" if the law was discussed prior to the fatal journey.
Former Bethlehem College student Caitlin Dickson, 19, and Tauranga couple Brian and Grace Johnston died in the accident and were farewelled on January 24 and 26 respectively.