And the Liberal Democrats Tim Farron is immediately challenging her over whether she agrees with her leader's view of the Iraq war. Of course, this is a perfectly run of the mill bit of political "gotcha" press releasing, of the type which all party frontbenches and press offices so enjoy indulging in, even if it can seem a little bit 'old politics' in its hyper-partisanship.
But perhaps the LibDems haven't done any research this time - as Next Left can re-reveal that Yvette Cooper was herself publicly critical of the policy decisions made over Iraq, stressing the need to learn the lessons from them for the future some years ago, well before Ed Miliband was running for the leadership of the Labour party.
Indeed, her views were secretly disclosed in a Guardian front-page report from the Fabian January 2007 new year conference'Labour must admit Iraq errors, say ministers', which rather demonstrates that the media have tended to significantly overstate the extent to which Ed Miliband and Ed Balls were breaking new ground in their leadership campaigns in their critical comments over the Iraq war. (As this blog set out back in May; for example, Ed Balls had argued on the record and in public that the weapons inspectors should have been given more time as early as the Fabian conference of January 2005, even if pretty much the same statement was treated as much more newsworthy five and a half years later).
At the Fabian 2007 event, Yvette Cooper's focus was on criticising the failures of post-war reconstruction and planning, an argument with which few would seriously disagree, as the Guardian report shows:
"I think if different decisions had been taken early on, we might have seen a different course of events. There would always have been difficulties in Iraq, but you should not underestimate the importance of people having a functioning economy - of having jobs to go to, people able to get food and to have a proper functioning infrastructure and how significant that can be to the course of events."
There were several similar points made at this time - very much fully acknowledged to be being made with the benefit from hindsight, which had not been available when the Commons was voting in 2003 - from ministers who argued it was important to address the lessons which could be learnt with hindsight.
Nor did these come from any one "faction" in the party. The 'Blairite' minister James Purnell was clear at the same Fabian event about the mistakes made over Iraq, including in the lack of legitimacy of how we went to war.
"There are many, many lessons we need to learn about Iraq and it is very important for us politically to recognise that. In terms of international politics, we need to learn the lessons of the mistakes that clearly have been made.
"I think the biggest mistake is that you always need to learn the importance of moral legitimacy and international support. Going back and looking at what happened, if we and the Americans had realised that the Iraq did not have weapons of mass destruction as an imminent threat, we would have had more time to get a second UN resolution we were trying to get. If we had gone into Iraq with international support, the situation would have been much much easier.
"It would have legitimised an intervention in Darfur in a way that it is now very very difficult."
And Hilary Benn, while defending the decision the government had taken at the time, also felt it was important to acknowledge the criticisms.
"The current situation in Iraq is absolutely grim, so let us be clear about that truth. Look, the intelligence was wrong, the de-Ba'athification went too far, the disbanding of the army was wrong and, of course, we should have the humility to acknowledge those things, and to learn. I am not insensitive to the huge well of bitterness and anger from lots of people in the party."
So I would feel confident that Yvette Cooper will want Labour to consider seriously the lessons from the report of the inquiry into the Iraq war which the last Labour government did (finally) commission, with Fabian pressure helping to get there is the end.
I am sure too that this is precisely what our Liberal Democrat friends would want her to do now.