The paper's vigorous and personal campaign against the party and Neil Kinnock in 1992 did influence the tone of that low campaign, though the paper later did acknowledge that its famous headline had overclaimed. And I doubt that Labour's inability to persuade the voters that it could govern was primarily about the media attacks on it.
The academics agree - as this John Curtice paper on how much influence papers do and don't have shows. It is not that papers don't have a good deal of influence in framing debates - but this is much magnified by the power which the politicians attribute to them. And the ability to influence voters is often much exaggerated by media discussion too.
As Curtice writes.
There was little evidence that newspapers had much impact on the aggregate outcome of elections. Between 1987-92 and 1992-5 the net movement of voting preferences amongst the whole electorate was very similar to what happened amongst those who did not read a newspaper at all ... when it comes to the outcome of elections, the disposition of the press does not make much difference at all.
1997 was an interesting test case, because the 'Tory press' backing Labour offered an opportunity to study whether papers changing their minds influenced readers to change theirs. But the case for a decisive influence in 1997 was particularly weak.
The Sun had no choice but to back New Labour in 1997. A populist paper has no choice but to back a party if it thinks it is going to win.
And it could not back William Hague when he ran his rather unpopular populism campaign in 2001, even he was often largely running on Sun editorial policy.
So the paper is following the political weather more than making it - though it had a significant policy impact on New Labour because of how much weight was given to the symbolic importance of winning the party and keeping it on board.
Of course, this means that they know that David Cameron is favourite now.
So the Tories will champion their non-electoral milestone. And The Guardian will doubtless report it as a major story too. Newspapers do influence other newspapers, rather a lot.
Getting on to the bandwagon before Cameron has sealed the deal may mean that The Sun will want to extract a price from the New Tories too. But their EU policy is already mad as toast and completely incoherent. Still, freed from the Murdoch embrace, might it be time to look at how some of the detail of David Cameron's policy is happily convenient for the News International empire
But we are the underdogs now. Underdogs need causes to fight for - and sometimes they need enemies too.
The dividing lines in British politics just got clearer.