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His comments come in the wake of more than $500,000 of fines and reparations being imposed on the SDHB and a contractor after the incident.
In a Dunedin District Court decision the SDHB was fined $225,000 and ordered to pay reparation of $25,000, while Fire and Mech Contracting Limited (FMCL) was fined $247,500 and reparation of $25,000.
There was consideration by Judge Michael Crosbie of reducing the fine in order to increase reparation, but he accepted he had no jurisdiction to do so.
The board was taken to court earlier this year after the 2017 incident, which occurred during the decommissioning of an X-ray machine.
The board and FMCL had previously pleaded guilty to two charges under the Health and Safety at Work Act.
On May 24, 2017, the victim - a registered builder with name suppression - was tasked with the removal and demolition of a 30-year-old X-ray machine. He had contracted FMCL to assist.
While the company had done a risk assessment, it was scant, and the court was told in February the board had not handed over the machine manufacturer's manual, which was imperative to understand the hazards involved.
The fines and reparation were handed down by the court last week.
The fact sheet for the case said the victim, whose name and company were suppressed, hired FMCL to remove the machine, as he did not have the expertise.
FMCL had undertaken a risk assessment that was approved by the victim, project managers and the board, though the assessment was described as inadequate by WorkSafe.
While removing the machine, a company engineer asked the victim to cut a wire rope.
When he did, a spring-loaded metal plate crushed his forearm, breaking two bones and causing extensive nerve, tendon and muscle damage.
The injuries required hours of surgery on the day, and more later in the year.
His orthopaedic surgeon described his injuries as ''a permanent disability'', and the victim said his mental and physical recovery would be a long one.
Mr Fleming said yesterday he had apologised for his failure to meet the victim at hospital on the day of the incident.
''And it was actually as a consequence of a victim discussing the issues I realised how wrong that was for me as chief executive.
''A contractor had been seriously injured and I have personally apologised because I need to care, as chief executive, for everybody within our organisation, and we need to make sure everyone that is involved with us goes home safe.
''I should have personally shown some more direct remorse at the time.''
Mr Fleming said the board had immediately changed its processes when installing or removing specialist equipment to ensure specialists were employed for the work.
The level of the fine would also be a challenge for the cash-strapped organisation.
''That will have to come out of the DHB resources,'' he said.
''That's taxing to both myself, in terms of how to find it and the impact it will have, but it is really important to send a message that organisations like ours need to take this sort of thing very seriously, and indeed we do.
''We are not changing any services, we're just going to have to make it work.''
When questioned about any health and safety reports written after the incident, Mr Fleming acknowledged a draft report had been reviewed because of disagreement over its findings.
''There was a draft report with some findings we didn't agree with, and that report was reviewed.''
Fire and Mech did not respond to a request for comment.
It is the first time a Crown entity has been prosecuted for a workplace accident since changes to the Crown Organisations (Criminal Liability) Act 2002, which made public sector agencies subject to the same fines as any other business under the Health and Safety at Work Act 2015.
-Additionally reported by David Loughrey