Mr Bunton said the root cause of what happened with the board's $16.9 million fraud did not lie at Mr Thomson's feet and several of the chairman's predecessors should be feeling "very uncomfortable".
Mr Thomson is under threat of dismissal by Health Minister Tony Ryall after refusing to resign when asked to last week.
Mr Bunton expresses his views in an opinion page article in the Otago Daily Times today.
He said the minister clearly had Mr Thomson "in the crosshairs of his political point-scoring bazooka".
This was an unreasonable "heads-must-roll approach".
In another development, former health minister Pete Hodgson yesterday said any inquiry would tie up money and time better spent on improving health services.
His view was based on some "bitter experience" from being minister of fisheries during the scampi inquiry.
With staff focusing on such an inquiry, the cost would be borne in the slowing of improving health services.
What needed to be established was that the procedures of all district health boards had been updated to ensure their risk of fraud was lowered.
Mr Thomson said he would be comfortable with an independent inquiry, but also questioned its value.
"Would it make any difference, at the end of the day, if an inquiry sat in judgement? Probably not."
However, if somebody decided that was necessary, "I certainly wouldn't have any reason to complain about that".
Mr Hodgson said that as minister, once he learned of the fraud, his focus had been on looking at how systems could be improved rather than saying to Mr Thomson, chief executive Brian Rousseau and the board: "You have behaved badly. These guys got the crook".
Dunedin South Labour MP Clare Curran agreed there should be emphasis on all boards having adequate procedures to prevent such a fraud in future.
National's Dunedin-based list MP, Michael Woodhouse, said he did not have a view on the possibility of an inquiry into the causes of fraud.
He had every confidence Mr Ryall would act in the long-term best interests of the region and supported the call for accountability.
He had engaged in dialogue with doctors who had been expressing disappointment and disbelief that the fraud could have occurred at a time when they were trying to get as much value as possible out of limited resources.
They continued to question how the fraud could have occurred.
