The boy's paternal grandfather Christian Roberts told the paper the diagnosis came on Friday.
"I support my son. I want Neon to have whatever treatment is going to make him better."
Neon, who underwent an operation for his tumour six weeks ago, was due to start life-saving treatment after the surgery.
The High Court's Justice Sir David Bodey told the hearing he had intended to give his judgement on whether Neon should receive chemotherapy only or radiotherapy as well.
"Medical developments have now occurred regarding the possibility to receive said treatment for such therapies at the present time.
"This has changed the medical landscape. Nature is no respecter of the courts," the paper reported.
Ms Roberts went on the run with her son to seek alternative treatments.
They disappeared from Tiverton, Devon, last weekend and were found this week in Sussex, 250km away.
Jodie Leese of Auckland, who is married to Mr Roberts' older brother Mike, told the Herald on Sunday her sister-in-law was not averse to treatment for Neon.
She had taken the boy to Tiverton for natural treatment at a well-recognised clinic.
"She has been seeking treatment for him constantly," Ms Leese said.
Sally Roberts made her decision to seek alternative treatment after doctors told her about the possible side-effects of radiotherapy.
"One of the things the specialist said to Sally was, 'We're going to have to fry your boy's brain now', which was really very insensitive. That really stuck in her mind."
Mr Roberts' family in Auckland wanted the decision "to be right for everyone", she said. "It's not something any of us would even be prepared to give an opinion on what Sally should be doing, because only parents know what's best for their child."
Doctors want to start radiotherapy on Neon immediately as part of post-surgery treatment, arguing his chances of survival will be reduced significantly without it.
