The centuries-old requirement for two corroborating pieces of evidence to prove guilt was previously described as a cornerstone of public confidence in the criminal justice system by the rank-and-file Scottish Police Federation (SPF).
It had stated that its removal could open police and the public to "spurious and malicious allegations".
The Association of Police Superintendents (Asps), which represents more senior ranks, was also "not wholly convinced" by the case for scrapping corroboration.
But both now support abolishing the need for corroboration, which is seen as a marked shift in position by Holyrood's Justice Committee.
Independent MSP John Finnie, an ex-police officer and former SPF official, said: "This may be perceived as a change in position of the staff associations.
"In written evidence, the SPF said 'corroboration is particularly important in maintaining public confidence in the criminal justice system'. And, specifically relating to police officers but also members of the public, 'would risk exposure to more spurious and malicious allegations that would be harder to refute'. What has changed?"
SPF vice-chairman David Ross said: "I don't consider that we have turned our position completely from one of resistance to one of support. I think, as our understanding has grown about what we are talking about here, our position has moderated to the extent that we would support the removal of the requirement of corroboration, in general terms, in favour of the requirement for a sufficiency of evidence, across the whole of the evidence, to prove guilt beyond reasonable doubt."
Asps president David O'Connor said in written evidence that he remains "not wholly convinced of the case for the complete abolition of the requirement for corroboration".
Mr Finnie said: "I would take that as unconvinced. What is the position of Asps? Are you for it, or against it?"
Mr O'Connor said: "At this particular time we are more content with the proposals in moving forward, provided that as we move forward we are quite clear on what the marking rules will be. We have heard a great deal about not just looking at the quantity of evidence but the quality."
Mr Finnie said the staff associations' positions have clearly "evolved".
Mr O'Connor said: "At the outset of the debate we had concerns about the wholesale abolition of corroboration, and there has been some clarity brought to the debate.
"We had concerns that we would potentially end up with a case where you would have a move away from the criminal burden of proof to something more like the civil burden of proof.
"One of the key safeguards for us is that we're retaining the criminal burden of proof, that we have to prove a case beyond all reasonable doubt."
Committee convener Christine Grahame, an SNP MSP, said: "That was always the case. I'm surprised it's taken you a year to figure that out. I'm sorry to be rude but that was never on the agenda."
Conservative MSP Margaret Mitchell said: "There seems to be quite a movement in the position of Asps and the SPF."
Police Scotland deputy chief constable Malcolm Graham said that the top ranks support the abolition of corroboration.
"A larger number of victims would get access to justice, and that may mean more prosecutions. Almost 3,000 additional victims could be given access to justice."
Supporters of abolishing the requirement for corroboration argue that it could make it easier to bring cases of domestic abuse and sex crimes to court.
Lily Greenan, manager of Scottish Women's Aid, told the committee about the difficulties the rule causes.
She described one case in which a woman fled from her home into the street "with her clothes hanging off her". It could not be prosecuted because there was no corroboration that her alleged attacker was there at the time.
Ms Greenan said: "If a woman has been so badly beaten that her neighbours fear for her life, who runs into the street with her clothes hanging off her ... is not able to get into court because there is no corroboration that it was him who did it this time, then we have something wrong with our system.
"That's the kind of situation we want to address. That's what happened. It couldn't go to court because there was insufficient corroboration in relation to his presence in the house at the time of the assault."
She also told MSPs about cases of violence against women in which attitudes and prejudices sometimes had more impact on the verdict than the actual evidence.
"We're not usually talking about evidence as being the driving force for whether or not there's a conviction. We're talking about attitudes, we're talking about assumptions and we're talking about prejudice," Ms Greenan said.
"So the notion that removing the requirement for corroboration is in any way going to change that situation is a false notion."
That was echoed by Tony Kelly of law reform and human rights organisation JUSTICE Scotland, who argued that abolishing corroboration would not necessarily improve the "appalling" conviction rate for crimes such as rape.
"What seems to be focused on, in relation to abolition, is getting cases into court. No one really concludes that getting all of those cases into court will deal with the appalling conviction rate. I completely agree that at the root of that appalling conviction rate are prejudices, attitudes.
"That clearly is going to take further work before we get anywhere near addressing the root of that."