A photograph of Cairns - taken shortly after the Herald broke the news of the perjury charge against him on Friday - shows him carrying a clear plastic folder titled "BMC" and the names of McCullum and Schwalger.
The material involving the pair was obtained by the newspaper which quoted Cairns who confirmed his legal team was analysing the same information ahead of the perjury case to be heard in London.
Yesterday, the Herald broke the news that the Metropolitan Police, who will charge Cairns with perjury next week, were so concerned about a trial witness being potentially undermined that they contacted their counterparts in New Zealand.
Garth Gallaway, McCullum's lawyer, said the legal row with Fairfax Media had been settled yesterday and the injunction would remain in place for now.
He said the leak of material which was "clearly confidential between client and advisor is a troubling development".
"Ironically, Brendon remains unwavering in his desire to see the game be rid of match fixing," Gallaway said.
"His resolve to give evidence, if he is required to do so, in relation to the match fixing approaches made to him is stronger than ever."
David White, chief executive of New Zealand Cricket, issued a statement in which he said he could not comment on matters before the courts.
"However, I would like to say this: New Zealand Cricket supports Brendon McCullum.
"In particular, we support his right to privacy and client confidentiality, and we support his right to bear witness."
Schwalger worked with McCullum until earlier this year and could not be reached for comment.
Cairns did not respond to a request for comment about the information he obtained.
But in a statement last week, he said the perjury trial would give "an opportunity to face my accusers in an open forum, with some rigour and proper process around that, so that I can clear my name once and for all".
"I hope that, through this forum, significant additional information will be flushed out that will help people to better assess the situation, as well as the character and motives of the parties involved.
"But I have nothing to hide and I will do whatever it takes to once again prove my innocence."
McCullum is likely to be a key witness against Cairns if the perjury charge proceeds to trial in London.
He has given a statement to the anti-corruption unit of the International Cricket Council where he claimed to be approached by a former top player, dubbed "Player X", who asked him to fix matches.
Cairns has conceded that McCullum was referring to him, but has repeatedly denied match-fixing and described the allegations as "despicable lies".
The perjury charge stems from Cairns' successful defamation case in 2012 where he won substantial damages against Lalit Modi, the former boss of the Indian Premier League, over allegations of match-fixing.
