Despite a daily search by their owners, the dogs were not sighted until March 4 when they were seen mauling sheep in mānuka forest high on the hills.
Robson said 43 sheep had been confirmed dead.
They hoped three mauled sheep would recover, but 10 sheep remained unaccounted for in the block where the dogs were found.
Both Kane and Robson said they were unaware Williamson had been operating as a boarding kennel without resource consent and were "shocked" to discover the Central Otago District Council had granted the consent.
"It is now all about what has the council done to allow this to happen. With all their knowledge of all the dogs roaming and going to the pound, why was she not shut down?
"I think council has massively failed and that dog kennel is a huge risk to us, our neighbours, dogs and dog owners," Robson said.
Williamson said the owners of the dogs that attacked the sheep did not disclose to her their dogs were capable of digging under a fence.
"I'm upset because I have been blamed for something which I feel is unfair."
"I think some responsibility needs to go to the owners of the dogs," she said.
"I have said I will pay compensation for the sheep except if he [Kane] has insurance maybe I could pay the premium and the excess."
Williamson said there was a huge need for her dog-minding service in the area and dogs had rights, too.
"The dogs [in my care] are allowed to go down to the river and chase rabbits and have fun.
"We don't all have to [kowtow] to the sheep which are going to be put down in a year anyway," she said.
Big Dog Homestay is in the Central Otago District but part of Glenfoyle Station is in the Central Otago District and the other part is in the Queenstown Lakes District.
The attack on the sheep occurred in the Queenstown Lakes section of the farm.
Queenstown Lakes District Council spokesman Jack Barlow confirmed dog control officers had previously impounded three dogs in the care of Big Dog Homestay, and Williamson had reported lost dogs to the council six times.
Central Otago Mayor Tim Cadogan said "this is obviously a distressing incident and I feel great sympathy for the sheep and dog owners.
"I am aware that staff from both CODC and QLDC are working through the operational aspects of this incident and while this is occurring I won't be commenting further."
Williamson's neighbour, Christine Everest, said she had complained many times to the CODC about dogs escaping from the homestay on to her property, and feared for the safety of her pet dog and three heifers.
"We have got to stop this carnage before it happens once more," she said.
