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Cairns, who is on trial at Southwark Crown Court in London and denies two counts of perjury and perverting the course of justice, was claimed to have discussed spot-fixing during a meeting with McCullum in a Kolkata hotel room in 2008.
However, according to Rhodes, to whom McCullum admitted the approach three years later following an ICC anti-corruption briefing, the New Zealand captain's statement in February 2011 mentioned a "business proposition" but did not include an explicit reference to match-fixing.
Orlando Pownall, QC, Cairns' defence lawyer, read extracts from McCullum's statement to the court: "We had a general conversation and then after about half an hour he [Cairns] asked me if I knew anything about spread betting. I told him that I didn't. I initially thought he was taking the piss."
Cairns then started to explain using a pen and paper: "He was telling me you can make a great deal of money. He told me you could make between US$80,000 to US$250,000 a day. He told me that he had never done it on an international match."
Pownall put it to Rhodes that the conversation between McCullum and Cairns concerned betting, not an approach for McCullum to underperform in a particular match.
Rhodes responded: "The inference is in the statement. It is clear to me that an approach is being made by Mr Cairns to Mr McCullum."
"To fix matches or to underperform?" asked Pownall.
"Yes," said Rhodes.
"Where does it say that?" Pownall continued, to which Rhodes replied: "It doesn't."
When asked why he had not requested McCullum clarify what he meant, Rhodes stated he was not "in a position to put words" into his mouth.
The ACSU, Pownall suggested, had done "nothing" in response to McCullum's statement, although Rhodes said that, as an unsanctioned tournament, the Indian Cricket League (ICL) was beyond the jurisdiction of the ICC.
The allegations, Pownall suggested, were "potentially momentous". However, Rhodes argued that without corroboration from any other source they remained unsubstantiated.
Rhodes added that he had "no reason" to believe McCullum had not been telling the truth. However, he said that as a field officer, his job was simply to collect information - it was up to his superiors to investigate his findings.
Rhodes recalled that McCullum had met him in Nagpur, along with his then-captain, Daniel Vettori, whom Rhodes stated did not contribute to the meeting and had been attending to provide support for McCullum.
However, under cross-examination, Rhodes was shown a statement made by Vettori in February 2014, in which he said he had asked Cairns to buy him a diamond ring with the money he was owed for undertaking a promotional tour for an Indian toothpaste company after the Champions Trophy in 2011.
Asked why his evidence had omitted this detail, Rhodes said that he did not recall Vettori's comment. "What I am saying is that if Mr Vettori is saying to me that he said that to me in Nagpur, then I will accept that."
Rhodes told the court that he had not made any notes of that conversation, adding that he had lost his diary for 2011. He also admitted that he had not made a note of McCullum's request that New Zealand Cricket should not be told he was making a statement.
Sir Ronnie Flanagan, the current chairman of the ACSU, also gave evidence. He denied that Cairns had been made a scapegoat to deflect media criticism into his unit's lack of success in tackling corruption.
"Corners were cut, normal action was left to one side with a view to achieving the scalp of Chris Cairns," Pownall suggested.
Flanagan replied, "absolutely not", adding: "If scalp turns out to be an appropriate description, I think it is an absolute tragedy."
The trial continues.