Such a path would leave everyone else out in the cold facing the same chilling financial challenges, with no sense of warmth in sight.
Scotland and Ireland are already believed to oppose World Rugby's global league plans, mainly due to their objection with the crucial element of promotion relegation.
CVC's offer is thought to be based on the Six Nations being taken away from free to air television, with Amazon the likely pay-tv partners.
In a strategy dubbed 'Project Light', the Six Nations unions are said to have been in talks for the past 18 months over pooling their commercial interests.
Selling off to a private equity group will provide short-term cash injections, with some suggesting each union could net up to £100m, but such a move is not in the best interests of the global game.
Long term, it could also mean 30 per cent less revenue year-on-year.
Convincing individual nations to consider others was always going to be World Rugby's biggest hurdle - these latest developments proving just how difficult it will be to reach any form of agreement.
The upshot for the Southern Hemisphere nations is their pathway to a stronger financial future seems increasingly shaky.
Leading players from New Zealand, Australia and South Africa continue to chase lucrative salaries in the north and revenue streams are tightening.
Sanzaar nations are, therefore, desperate to secure what has been touted as a 40 per cent uplift in revenue – a boost of anywhere between £5m ($NZ9.6m) to £10m ($19.2m) anually, should the Nations Championship progress.
World Rugby outlined its controversial concept for the new tournament last Wednesday, saying it would start in 2022.
It would feature 12 teams in each of its three divisions.
The top division would be comprise a northern conference - the Six Nations sides - and a southern conference, featuring the four Rugby Championship teams and two others, expected to be Fiji and Japan.
Each team would play each other once a year, either through their own competition, or in one of the July or November test windows.
On this basis the Nations Championship would provide exposure to the likes of Fiji, and also include promotion and relegation to provide a pathway for emerging nations.
In other developments, after strong pushback from leading players concerned by their welfare, World Rugby is thought to have ditched the semifinal stage of the concept.
That would mean a maximum of 12 tests per year for the two finalists – 11 for others.
Outside those commitments, the All Blacks and Wallabies would still be permitted to play one extra test in order to contest the Bledisloe Cup each year.
Unless Six Nations powerhouses can be convinced to vote for a global way forward, though, such details will be purely academic, and it could be back to the drawing board for the financially struggling southern nations.
The Nations Championship could now be a dead duck.
