If only it had been true.
Blair-Brown tensions remained a dominant frame for discussion of the Brown government. These were ultimately stabilised as a new Brown-Mandelson rapprochement restored New Labour to its natural unsteady state as a duopoly project in Blair-Brownism, from 1994 to 2007, and again from 2008 to 2010.
Three years on, his Brownite history did a good deal to scupper Ed Balls' chances of getting a competitive run in the Labour leadership contest.
That Balls ended his unsuccessful campaign with an enhanced reputation, even with many political opponents was largely because he did not run as a Brown continuity candidate, instead establishing his own voice, and reputation as a hammer of the Coalition. (This was one reason why the Ed Miliband campaign quickly discarded the early idea of explicitly pitching a "unity" candidacy as their central narrative).
All of that makes some of the comments quoted Dan Hodges' feature in this week's New Statesman suggesting the party may be on the brink of a new round of factional civil war - Ed versus Ed, ex-Brownite versus ex-Brownite no less - very odd indeed.
"Ed Miliband's team are terrified of Ed Balls and Yvette", says one Brownite insider. "They think they're going to come and try to kill him. And the reason they think that is because they will."
That may be good copy - but it makes no political sense at all.
Whoever may have spoken to Hodges, and from whatever motives, they could hardly have devised comments better designed to be damaging to their supposed beneficiaries (were they to be taken seriously).
Next Left has undertaken detailed linguistic analysis of the piece. This - mainly the obsession with violent killing metaphors - strongly suggests the secret sources are blokes, and indeed blokes' blokes at that.
I rather suspect Yvette Cooper might want to be a million miles away from such hyper-macho posturing.
Indeed, this may be the daftest point in the full (print edition) piece.
"They're already organising," says one shadow minister. "Yvette has been contacting all the teams identifying one member to be her link person. The cover is she's doing it as part of the women's brief. But everyone knows she's building a base."
Does anyone seriously think its a bad idea to have a link on gender equality in every shadow team? You can't get much more Old Politics than that.
Dan Hodges certainly enlivens our political blogosphere. He can write. As readers of Labour Uncut will know, the media-savvy controversialist loves to make a splash, perhaps a legacy of his time in campaigning and PR. And, however wrong he might turn out to be - as with his exuberantly calling the leadership contest for his candidate David Miliband - you can guarantee that he will climb straight back onto the horse.
Hodges has never run with any "Brownites" - he is a left Cruddasite who seems to like a bit of Blairism on the side. He seems a rather curious choice for a couple of Brownites to suddenly choose to unburden themselves and to open up to him with secret murderous desires.
More importantly, there is no such thing as Brownism now.
Gordon Brown, adjusting to the role of an ex-premier will no doubt make contributions on the international economy and global development, while wisely steering clear of domestic political contention within Labour. But his once tremendously close-knit political tribe - there were never more than a dozen people who could properly be called "senior Brownites" - has scattered in every direction. It provided two different leadership candidates, and the campaign manager of the David Miliband campaign too, and splitting three ways (between David, Ed and abstention on the final leadership ballot).
Blairism lost all sensible meaning contemporary meaning some time ago too - a point well made by Charles Clarke two years ago. What is illuminated about the diverse political views of (say) David Blunkett and John Reid, David Miliband and Alan Johnson if one labels them as "Blairites"?
It is not just about people moving on. The Blair-Brown labels speak much more to the central political concerns of 2001 than than those of 2011. Blair and Brown differed over public service reform (but not increased spending on the NHS and schools), as well as redistribution (while sharing an ambition to end child poverty), and earlier over the EU and the Euro.
But they didn't differ much over the New Labour economic settlement; home affairs and civil liberties; nor particularly over issues - industrial strategy; a low carbon economy; housing; social care and demographic change; political reform after 2001 reforms - which were somewhat marginalised under New Labour, because neither of the Downing Street factions saw them as priorities.
The paradox of post-factionalism
If Ed Miliband's new generation is to mean anything, it must mean moving on from the hyper-factional culture which did disfigure the high politics of New Labour, as the intense debate between two small tribes
But the paradox of post-factionalism is this: everybody first judges how serious you are about leaving all of that behind by counting the heads from the old factions.
The new leader could hardly have been more accomodative towards those who did not support him - with Alan Johnson as Shadow Chancellor and Liam Byrne running the policy review, rival candidate Andy Burnham as elections coordinator. Ed Balls and Yvette Cooper are shadowing the other great offices of state.
His Shadow Cabinet - because it lacks Jon Cruddas, and not just David Miliband - is a little short of voices to the left of Ed Miliband, Balls and Cooper. (All three would be regarded as within the Croslandite tradition of the egalitarian Labour centre-right in any sensible analysis).
What Ed Miliband needs to do, over the next two years, is to remap the contours of party debate. The leader should seek to expand the "squeezed middle" within his Shadow Cabinet, and within the Labour party too. And it is precisely his central theme of finding an effective political and policy strategy to address the squeezed middle - and what that means for political economy, and a contributory welfare state - which can create a new central spine through the shadow cabinet which could remap the Labour debate. The are concerns which has been addressed by Jon Trickett from the left, and over a period of time by John Healey, John Denham (who worked on long-term policy for the Ed Miliband campaign), Douglas Alexander (David Miliband's ex-Brownite campaign manager) and Liam Byrne on the 'right' of the party, and in charge of the policy review.
The case for factions - without factionalism
If the Labour party's debate is thought to be conducted between the Progress right and Compassite left, then that might often be a rather partial and incomplete one. Many - probably most - party members will find themselves in the "excluded middle".
Compass have in the New Statesman piece been very quick to again overclaim Ed Miliband as "ticking all their boxes" or "singing their greatest hits" having spent the summer leadership contest publicly unenthused by any of the candidates before the result was known).
But that is not to say that these perspectives from the left and right do not represent legitimate arguments within the Labour debate. There are bound to be a different views within broad governing parties. Loyalty to leaders is important in party politics, but loyalty is not enough. It can lead to a rather plebiscitory and top-down politics with little sense of what it wants footsoldiers for.
For me, the key distinction is whether different strands of party opinion accept that other views within the party have a legitimate voice in a broad and plural party, rather than dismissing them as heresies which must be purged in favour of the true faith, or the only possible path to election victory.
So that "Compass v Progress" frame is especially unsatisfactory and unproductive if and when voices from left and right seem to have more to say about what is wrong with an (often caricatured) view of the other 'wing' of the party than in making their own constructive case. (The party got stuck spending several years after 2005 debating whether it would be dangerous to appeal to 'core votes' or 'swing voters', succeeding in ending up appealing to neither as we hit 29%).
The Labour party will need to adapt to a more pluralist political environment. A greater level of comfort with internal pluralism will need to be an important part of that if Labour wants to be a broad party, and one capable of forming links beyond party politics too. So there is not necessarily anything wrong with party pressure groups and informal campaigns pressing on issue or another, or indeed with strands of party opinion and 'factions', if factionalism can be avoided. One good example is Compass and Progress are showing they can work together in campaigning for Labour supporters to vote Yes for the Alternative Vote.
So its not quite death to the factions. But let's leave the assassination fantasies to the RSC. And you can certainly forget about a party civil war when nobody has any footsoldiers ready to fight one.