Referring to Burden's departure from St Peter's, Stratford said the board was aware of the "negative media attention" he had received.
As part of the appointment process, the board had spoken to referees and checked reports from independent parties, he said.
"This decision was based on the character, mana and reality of the person that was revealed to the Board during the recruitment and interview process, not on any subjective online commentary," he said.
However, some parents expressed concern about Burden's appointment and the board's comments.
A mother who had two children at the school told the Herald she was "horrified".
"People can change and move on, but this was a WorkSafe issue, they found there was cause for investigation. And then there were findings that came out of the investigation. This is a little bit different than a whole group of parents complaining in the media."
The mother, who asked to remain anonymous to protect her children, said she was not reassured by the board's comments.
"It was as though they were defensive about it, and sort of brushed off mentions in the media when in fact it was more than that - it was a WorkSafe investigation."
Other people related to Howick College expressed their opinions about Burden's appointment on the school's Facebook page.
"Shocked by this appointment," one person said. "A dreadful decision," said another person. "I feel for every teacher and pupil."
When asked about parents' concerns, Stratford said St Peter's had completed an investigation into allegations of bullying against Burden.
"Through the recruitment process, the board received advice that gave us confidence bullying is not part of Mr Burden's leadership style," he said.
The board also considered WorkSafe's report and sought clarification from the watchdog, he said. He acknowledged that some people were still uncertain about the appointment of the new principal and the board was happy to talk through its decision and answer any questions.
"Mr Burden is very aware of the scrutiny that surrounds his appointment," he added.
The investigations at St Peter's came to light after Burden and his wife and deputy principal Yevette Williams had been mysteriously absent from St Peter's for several months, beginning in term 1 last year.
After receiving an initial complaint of bullying in December 2020, WorkSafe did not launch a formal investigation but sent specialist health inspectors to the school in early 2021 to speak to staff and the board and check the school's policies and procedures. The inquiries were not focused on specific individuals but on the school's processes.
A summary of its 1000-page report, obtained under the Official Information Act, described the initial complaint as "serious". Another 14 complaints were received over a six-month period from existing and former staff, former board members and parents.
In the first meeting with WorkSafe officials, Burden, Williams and former board chair John Erkkila maintained that there was no truth to the allegations.
After a six-month process, WorkSafeconcluded that there was allegedly problems around staff wellbeing and the complaints process at the school.
"Several workers, ex-workers, parents and past board of trustee representatives came forward to share their experiences of bullying they had experienced or witnessed," the WorkSafe report's summary said.
"Although the experiences differed, the theme remained consistent that St Peter's School allegedly had a poor culture in relation to staff wellbeing and there was fear amongst staff to speak out about their concerns."
Burden and Williams resigned in May, before the inquiries were completed.
By June, the board and senior leadership at the school "appeared committed" to making changes, WorkSafe's report said. It later reported that the school had improved its policies and procedures.
Since leaving St Peter's, Burden has been working as an education consultant and advising a Melbourne education institute. He was previously headmaster at Mt Albert Grammar and Westlake Boys High School. After leaving St Peter's, Williams enrolled in a PhD programme on education leadership.