The organisation, which claims to represent employers of all sizes throughout the UK, initially joined the anti-independence campaign by registering with the Electoral Commission, something that's required to allow them to spend up to £150,000 campaigning for a No vote in the referendum.
This led to an exodus of its members who wanted to remain neutral in the debate. Businesses including Aquamarine Power, a clutch of Government agencies, and the majority of Scotland's universities all quit the CBI.
Crucially, the BBC and STV both took a similar stance. As our national broadcasters they must guard their impartiality if they're going to have public confidence as sources of news coverage.
Remaining members of an explicitly anti-independence campaign body like the CBI would have been unthinkable.
Since then the CBI has done a rather clumsy U-turn. Blaming the whole shambles on a junior member of staff, they have asked for their registration to be withdrawn.
It'll be interesting to see whether they make any effort in future to adopt a genuinely neutral stance on the referendum, or if they just carry on working for a No vote regardless.
But the whole affair has exposed some deeper issues about the CBI, and begs the question, why did these organisations ever join it.
The truth is that the CBI is not - and never was - just a business networking organisation.
Take a look at its website, and you'll see what I mean.
Over the last year alone, its press releases include explicitly pro-austerity arguments, praise for the UK Government's fiscal plan, calls for privatisation of Scotland's public services and its publicly owned water utility, and demands for tax cuts and deregulation.
It's perfectly clear that, referendum or no referendum, the CBI is an economically right-wing lobbying group, openly advocating free-market ideology.
Indeed, their Scottish director (whose recently announced early retirement has, they say, nothing whatsoever to do with their chaotic repositioning on the referendum campaign) was recently challenged over the gulf between rich and poor in the Scottish economy, and answered by describing equality as an "abstract" term, openly admitting that while he read a lot about it, he didn't really know what it meant.
Of course he doesn't - he's a former banker who's spent the last 20 years representing the interests of those who are very well served by the same economic system which causes inequality.
If membership of the CBI isn't compatible with a broadcaster's neutrality on independence, it surely can't be compatible with their neutrality at election time either.
The organisations which have quit the CBI should take this opportunity to reflect on what they were ever doing on its membership books in the first place.