The council has been split 5-4 several times this year on issues related to the project.
Before yesterday's vote on whether the HBRIC "reforecasting" agenda item should remain secret, HBRIC chairman Andy Pearce told the meeting matters in the associated paper were commercially sensitive, including the size and nature of a commercial adviser's fee.
Council chief executive Liz Lambert said the question around which matters on the agenda should be kept secret "took quite a while to resolve".
"We're always acutely aware of the huge public interest in this whole area and don't for one minute envisage that all the information - should you decide to pass the recommendations in here - that all of that will remain in public excluded," she told councillors.
"There will be an opportunity for the broader outcomes to potentially be made public sooner rather than later."
Mrs Scott, the council's deputy chairwoman, said she supported discussing the item in private because it was important the council had the chance to understand it fully.
"It places us in the position where we can question some commercially sensitive information which we would not be able to gain answers from if we were in public. We need to be able to have the confidence of the [HBRIC] board that they can answer the questions that we ask with the assurance that we are not going to repeat it outside that forum until it is appropriate to release that information."
Mr Graham said the public had a right to know how the council was spending its money.
"I am not going to be taking part in this farce anymore," he said. "They [the other five councillors] can go and have their own little discussion. I'm not going to participate in this blatant transgression of the democratic process."
Mr Barker said: "I was looking for a compelling case as to why the public should be excluded and I didn't get it."
Mr Beaven said there was "distrust and antipathy" from the public towards the project due to the council not being open enough.
"This is a continuation of it and it's really frustrating.
"You get to the point where you have to make a stance of some sort to bring attention to the issue."
Mr Belford said attending closed-door sessions was unhelpful for councillors because they could not share with constituents what they learned.
The council has committed to invest up to $80 million in the Ruataniwha scheme if conditions are met, including that sufficient funds are raised from other investors and enough CHB irrigators sign up to make it viable.
Mr Wilson last night would not say what had happened in the public-excluded session.