"Because of that we chose to close — we won't do the Government's dirty work," Mrs Fifield said.
The couple, who are unvaccinated themselves, said they would not "discriminate" against people who chose not to accept the vaccine.
Council chief executive Sharon Mason said Mrs Fifield was entitled to comment in her private capacity as a gym owner.
"But she was not speaking on behalf of Buller council and her personal stance is not one that Council shares — the council encourages all staff to be vaccinated."
The council was following Ministry of Health guidelines and using its risk assessment framework, Mason said.
"We are also working closely with the District Health Board to encourage our community to become vaccinated."
DHB chairman Rick Barker said Mrs Fifield's reference to the Government's "dirty work" was unwarranted, in his view.
"I don't agree with that. We are talking about a virus that has killed more than five million people and the Government has to take it seriously — it has a responsibility to protect public health."
Barker said it was only the protective measures taken by the Government to date that had saved New Zealanders from the ravages of Covid seen in other countries.
"In Italy, for instance, it's wiped out a whole generation of older people. We don't want that here."
Barker said in his own family he had been forced to draw a line in the sand over vaccination.
"I have a relative who has chosen not to be vaccinated against Covid and I have told them they are not welcome to return until they are."
That was not a matter of discrimination but a matter of protection for himself, his wife and any family members or guests under his roof, Barker said.
"Presumably she has rules that discriminate against smokers — if people came in smoking big fat cigars she'd ask them to leave because of the health risk. That is no different from keeping out others who pose the health threat of Covid."