Pathologists for the police thought it was brain tissue, but suggested the evidence be reviewed by a neuropathologist, according to the document read out by Mr Hislop.
The New Zealand scientist who looked at the samples said the tissue, found 58 days after the murders in August 2000, was too degenerated to identify as brain tissue.
According to the document - which was not disclosed to defence lawyers at Lundy's original trial - the neuropathologist, Dr Heng Teoh, said Lundy should not be convicted on the forensic evidence he viewed.
Mr Grantham was later given permission to fly to Texas to show the samples to Dr Rodney Miller, who gave damning evidence about two specks of tissue found on one of Lundy's polo shirts.
Mr Hislop told the Privy Council the science used by Dr Miller to identify the tissue as brain tissue was "fundamentally flawed".
He said the police document was at odds with the Crown case that the DNA well preserved and was a "substantial development".
"Detective Sergeant Grantham was very alive to the value of this information to the defence. He chose to not disclose it," said Mr Hislop.
Privy Council member Lord Hope, described the discovery of the document as a "striking revelation".
Lundy, now 54, is serving at least 20 years in prison after being convicted of the axe attack in his Palmerston North family home.
The Privy Council hearing is set down for three days.