The top two sides in the global rankings are not due to meet until November next year but the RFU wanted to bring them together sooner and Jones, as head coach, gave his support for the plans last weekend.
Such was Ritchie's apparent determination to push through this additional Test, there were fears that the RFU board would veto the Barbarians-New Zealand fixture - not just at Twickenham but anywhere in London.
That in turn would have diminished the anticipated revenue if the game was moved outside the capital - which is home to a large antipodean community.
Tew has been so set on the matter - no doubt reflecting the wishes of All Blacks head coach Steve Hansen - that it appears the RFU have been forced to back down and abandon attempts to force through an England v New Zealand showdown this year.
As the national governing body, they have to approve all matches within their jurisdiction, but exercising their right to veto the Barbarians game would have left them open to accusations of being heavy-handed and churlish.
There are concerns within the RFU that allowing the world's premier team and box-office favourites to play at Twickenham prior to England's campaign against Australia, Argentina and Samoa may adversely affect ticket sales or corporate hospitality profits.
Yet Ritchie and his fellow executives have seemingly pulled back from the brink by letting the game go ahead.
Since Sportsmail reported that the RFU were trying to arrange for Jones's side to face the All Blacks, there have been widespread suggestions that their motives were purely financial.
However, that was a dubious claim, as the additional Test would have entailed an unprecedented fee to the NZRU and also demands from the Premiership clubs for a 50-50 split of all profits in return for releasing their players outside the official window.
England have not played New Zealand since November 2014, so by the time they next meet, there will have been a four-year hiatus. The countries will now contest just one match in this four-year World Cup cycle, having locked horns six times in the 2011-2015 cycle.
Jones insisted last weekend and again on Monday that he was very keen for his record-breaking team to take on the game's pre-eminent force.
But there had been criticism of the plans owing to the thorny issue of player welfare - and now that it appears the fixture won't take place, the Australian can proceed with his stated intention of resting some of England's Lions contingent, which should be substantial, during the autumn series.