For this reason police have not disclosed exactly how Ms Jefferies died so that they can discount such confessions.
However, Mr Whitely said outside court that the false confessions still consumed an enormous amount of police time because it was vital to take them seriously.
"We need to make sure that they're not actually [telling the truth]. Wouldn't it be horrible if the person's told me they've done it and I've eliminated them? That's the reason we're protecting the cause of death so we don't get caught out like that.''
Police have previously said Ms Jefferies' death was "highly unusual''.
Coroner Gordon Matenga agreed that disclosing how she was killed could compromise the ongoing police investigation and ordered the exact cause of death be suppressed.
The inquest was told that Ms Jefferies, 22, was known to police as a woman who led a dysfunctional lifestyle, and regularly drank and used illicit drugs.
She often met friends and drank at the reserve, which was near to her mother's house, where she lived with her 1-year-old son.
She was last seen on the evening of July 10, 2005, by her mother, who did not find it unusual when she did not come home that night.
Police have been unable to establish her exact movements between then and the time her body was found by a man walking his dog about 36 hours later.
She was wrapped in a red tarpaulin and a black rubbish bag. A yellow PVC raincoat, a piece of plywood board and a framed wooden picture were also found at the scene but examination of these items has been fruitless.
A post-mortem established that Ms Jefferies did not die there and her body must have been dumped after she was killed elsewhere else, the inquest was told.
More than 750 people have been interviewed by police - many have been spoken to more than once - and around 60 remain "persons of interest'', Mr Whitely told the inquest.
Police even offered a $50,000 reward for information which led to an arrest, but this was withdrawn in 2007.
Mr Matenga said the evidence that Ms Jefferies died at the hand of another was conclusive.
"There is insufficient evidence to establish any other of the circumstances of her death. This is through no fault of the police; in my view their investigation carried out to date has been extensive and thorough.''
Mr Whitley told reporters he was still hopeful of solving the case, which has been a constant part of his life for more than six years. "I continue to get information and I've always said that we'll only get there with the help of the public and one day... the piece of the jigsaw puzzle that we've been waiting for is going to arrive on my desk and we'll be away.
"I want to be able to get a result for Katrina's family.''