The high-school student who left Auckland in alert level 4 to get to Dunedin is understood to be a rugby player who arrived just before a big game.
Otago Boys' High School is due to play Nelson College in the South Island secondary schools' final in Dunedin on Saturday.
Otago Boys' has not confirmed any link between the match and the student, who arrived in Dunedin last Friday.
A statement from rector Richard Hall on Tuesday made no mention of rugby.
The pupil's appearance at school on Monday alarmed staff. He was tested for Covid-19 and returned a negative result.
He has been in isolation this week.
Hall has said the student "may not" have obtained an exemption to travel from Auckland and police are investigating whether a lockdown breach occurred.
Health officials have not said when his isolation stint is likely to end.
Otago Boys' said yesterday it would seek independent scrutiny of the sequence of events, which included the student staying at the school's boarding hostel on Sunday night and turning up for class the next day.
The school said the student stayed with whānau on Friday and Saturday nights.
"The board is engaging an independent person to conduct a review," Hall said.
"We will respect the privacy of the individual involved and will not be commenting any further on his activities."
Board of trustees chairman Lawrence Alloo said the school was working with the Ministry of Health and other agencies and investigations were continuing.
"We have nothing to add at this stage."
Southern District Health Board medical officer of health Dr Susan Jack said the student was being managed in accordance with public health advice and in conjunction with the school.
"We will not be commenting on individual details for privacy reasons."
Jack has called the situation low risk and the Ministry of Health highlighted there had been no recent cases of Covid-19 in the South Island.