One of the grandmothers of missing four-year-old Gus Lamont says police have a theory that she buried her grandson after an accident — an allegation she describes as "ludicrous".

Speaking publicly for the first time, Josie Murray told Seven News's Spotlight program that police should instead investigate the possibility her grandson was abducted from the family's remote property south of Yunta, in South Australia's outback

Gus was reported missing from his family's property, Oak Park Station, on September 27 last year.

Last month, the head of SA Police's Major Crime Division, Detective Superintendent Darren Fielke, said one of Gus's grandparents remained a suspect in the police investigation into the boy's disappearance.

Police have previously said they believed Gus had not wandered off from the homestead and there was no evidence he had been abducted.

Ms Murray, 75, told Spotlight she was not involved in Gus's disappearance.

The network asked if she was the main suspect.

"They've said that they don't think I hurt him; they think that I buried him," she said.

"That's one of the theories they're working on and, as I say, for so many reasons, it's ludicrous. It just doesn't make sense. 

Police will not discuss specifics

In February, Josie Murray and Gus's other grandmother, Shannon Murray, who also lives at Oak Park Station, released a statement saying the family had "cooperated fully with the investigation and want nothing more than to find Gus and reunite him with his mum and dad".

On Sunday, SA Police said the investigation into Gus's disappearance was "one of the largest and most intensive undertaken by SA Police in connection with a missing person".

"It has involved an unprecedented level of ground and air searching across a very large search zone and utilised unlimited resources and the expertise of multiple other agencies and organisations," it said.

SA Police said because the investigation was ongoing it was "not appropriate for SA Police to discuss specific aspects of the investigation that could compromise any potential future court proceedings".

The Adelaide Magistrates Court fined Ms Murray $10,500 earlier this month for possession of a gun silencer at the family's property, but police said the matter was unrelated to Gus's disappearance.

Suspicion put on police work

Ms Murray told Spotlight she noticed that an old bed frame at Oak Park Station had been moved after Gus's disappearance, along with a weather station.

She also said she saw wheel tracks of a medium-sized car going past both locations, but, because of the large number of vehicles that had entered the property to search for Gus, the evidence had been overlooked.

"I thought that's strange too and I started to think almost immediately 'I wonder if someone's come in?' and all the time I was thinking there's a chance he's been taken by someone," she said.

She said she saw also saw a footprint in one of the dam's muddy shores, but police dismissed it as being made by a diver. 

"He must have had tiny feet," Ms Murray said.

Another theory put forward by family friend Bill Harbison was that a wedge-tailed eagle took Gus.

"A wedge-tailed eagle can pick up a 20–25-kilogram kangaroo and take it without much difficulty; Gus was 13 or 14kg so a mature wedge-tailed eagle would find that quite comfortable," he said.