Mitchell Starc on Tuesday became the first player from the 2018 team to reject Usman Khawaja's claims of widespread knowledge and prior use of sandpaper.
Test greats Mike Hussey and Mark Waugh also backed CA's call not to reopen the investigation, as Adam Gilchrist stressed the importance of the game moving on.
Khawaja's claims in his memoir Sabr contradicted CA's findings that only Cameron Bancroft, Steve Smith and David Warner were aware of the plan.
But speaking on Tuesday morning, Greenberg reasoned a fresh investigation into the events of March 2018 would simply land officials back in the same position.
"When you cut to the core of the challenge that we face here, Usman's version of events is inconsistent with what others have had to say," Greenberg said on SEN.
"Usman is passionate and committed and ... that is commendable and understandable.
"I can assure you there are lots of other players who have a very, very different version of events. And they have made that very public from the very start of 2018, they have been very consistent in their position right through until today.
"From my conversations with many over the weekend, I don't think that will change either."
Already, Greenberg's prediction is playing out.
Warner this week said Khawaja's recount was "100 per cent accurate", while also hitting out at the initial investigation and labelling it "rushed and botched".
Reserve bowler from 2018 Chadd Sayers also backed Khawaja's version, while Bancroft in 2021 said it was "self-explanatory" when asked if the bowlers knew about the use of sandpaper.
But the public position of other players has been that they were unaware, with Starc, Pat Cummins, Nathan Lyon and Josh Hazlewood adamant of that in a 2021 statement.
Starc maintained that position on Tuesday, insistent he and the rest of the bowlers only became aware of the use of sandpaper when Bancroft was caught on field.
"We (the bowlers) weren't aware anything was taken onto the field to be tampered with," Starc said at a Kayo Cricket launch event.
"We saw (the sandpaper) on the big screen in Cape Town.
"As far as the book is concerned, I haven't read it. I probably won't read it. So that's for Usman to elaborate on."
Starc also admitted it was "definitely disappointing" to be talking about the issue again on the eve of the summer, some eight-and-a-half-years on.
In the past two days, Scott Boland, Nic Maddinson and Marnus Labuschagne have all been asked their views on Khawaja's book.
Mitch Marsh is expected to speak later this week and will face the same questions.
But Greenberg is well aware this won't be the last time the issue is in the headlines.
"I am sure David will release a book ... it's highly likely our captain will release a book at some point. Others will also release a book," Greenberg said.
"What we will read is differing versions of events. That's what we're dealing with right now. I don't think many people can get their head around it.
"The same time, in the same location, in the same incident, people have very different views of what happened and recollections of what happened.
"And how we can account for that is a challenge we are sitting right in the middle of the vortex today."
Greenberg also confirmed he had been aware of the differing views since he became players' union boss in 2020 and had read transcripts from the 2018 investigation.
In the time since, CA's board, management and high-performance unit have almost completely changed.
"We don't see any compelling reason to open the investigation or revisit this again. I don't think there's anything that can be gained from that," Greenberg said.
"The chapter was difficult. But there is absolutely no benefit in going back. That's the clear position of the CA board. It's time we have to look ahead.
"We have said we're comfortable with the outcome of the investigation based on the information we've received.
"That includes what we've seen from Usman and our position hasn't changed on that."
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