Monarch Funeral Home director Lance Shearman said Tararua District Council had admitted an error and he had helped them fix it.
"They and I have helped the family endlessly through the situation and through the process. There has been a suitable and positive resolution."
Mr Corkin had been buried in a plot next to David Pocock's, but the mistake around the boundaries of the two sites meant Mr Corkin's plot appeared to have the Mr Pocock's headstone.
Mr Pocock was buried at Mangatainoka Pahiatua Cemetery on September 25, 1998, aged 15.
Tararua District Council chief executive Blair King said the two plots had ended up with "crossed boundaries".
"Local knowledge" had led to the family and Monarch Funeral Homes being alerted to the mistake.
Permission was granted by Mr Corkin's family and the Ministry of Health before the disinterment on Wednesday.
"The family were involved in the decisions right through, and we appreciated their co-operation," Mr King said.
"In an issue like this it is the family who are first and foremost affected."
He wasn't aware of any other problems with plots at the district's cemeteries.
"It comes down to how accurate the records from historical records are," Mr King said.
As technology developed the risk of mistakes decreased, he said.