A discussion paper about the pilot was brought to Friday's DHB meeting.
Board member Michael Laws wanted to know what the nature of the medical staff's concerns was.
Mrs Patterson said she did not want to discuss this in public because it would involve talking about an individual staff member.
Board chairwoman Kate Joblin agreed that the public section of the meeting was not the appropriate place to discuss this particular issue, but Mr Laws did not accept that.
"This scheme was announced and promoted publicly. It has now publicly been canned, again without reference to the board. I don't accept the rationale that it be discussed in confidence."
Board member Ray Stevens suggested the problems arose because the natural therapy pilot was promoted on a website about witchcraft and wizardry.
Mrs Patterson confirmed this was the case.
"We were well motivated to do something a bit different for staff, something they enjoyed and are already mourning the loss of. However, when you have a senior staff member with a qualification that the public should be able to rely on, linking our programme to wizardry and witchcraft, then of course we have a problem.''
Some board members expressed the view that the board should have had the opportunity to approve the pilot before it began.
But board member David Warburton said the pilot was about staff, and therefore was a management issue.
"If this was set up for the public, then it should have come to board. But this was about staff, so I accept that it was for management to deal with."
Both Mr Laws and board member Clive Solomon condemned the natural therapy pilot as being "supernatural" and "witchcraft".
"If you think traditional western medicine is the only form of medicine, that's your view, but I disagree," Mrs Joblin said.
"Then you should resign from the board," Mr Laws replied.
Mrs Joblin said in hindsight she accepted that the issue should have come to the board.
In response to a question from board members, Mrs Patterson said if the trial had been successful, a proposal would have been brought to the board around offering natural therapy to patients.
"We do believe a number of these therapies have a place for patients who choose to use them, for example, for pain relief," she said.
Board member Clive Solomon objected to this but was prevented from speaking by Mrs Joblin, who said she wanted to move on to another item on the agenda.
Mr Solomon walked out of the meeting and later told the Wanganui Chronicle he was tired of serving on a board with "utterly incompetent leadership".
"[This] natural therapy clinic has sadly made our hospital the laughing stock of serious medical practice in New Zealand," Mr Solomon said.