The Leveson inquiry is not a judicial investigation into Rupert Murdoch’s political opinions. It is supposed to be looking at media ethics.

The two subjects overlap in one sense: Murdoch’s views substantially influenced – dictated in some cases – the editorial lines taken by the newspapers he owned. If politicians changed their policies just to court the support of those papers, bowing to the whim of their proprietor, democracy was worse off.

But even in that analysis it is the nature of the influence, not the beliefs themselves that would be intrinsically pernicious. Or, put another way, Rupert and James Murdoch are allowed to hate the BBC and Ofcom and think that the licence fee is a neo-Stalinist tool for state control of the media. They might be wrong, but the view itself only becomes problematic in a way that is relevant to Leveson if government policy was bent to accommodate the prejudice in exchange for News International support. If there is a transaction of some kind, it is corrupt. There is grey area of course. Transactions in politics are often implicit. Nothing need be said. It is understood, but never written down, that certain choices will yield certain outcomes. Getting to the bottom of that will be one of Lord Justice Leveson’s biggest challenges.

The Conservative leadership is avidly pushing the narrowest possible definition of that perceived transaction. One of the most important moments in George Osborne’s evidence [2] to Leveson yesterday came when he denounced the theory that there was some “vast conspiracy” to hand full control of BSkyB to the Murdochs. This view, in the Chancellor’s words, “just doesn’t stack up”. It was an important précis of the government’s main line of rebuttal around the whole Leveson/phone-hacking debate.

Essentially, Number 10 wants to control the political argument over what constitutes an “improper” relationship with the Murdochs. That is: the allegation that there was a specific, explicit pact in which News International newspaper endorsements were procured with willingness to permit the BSkyB takeover. As long as no documentary evidence surfaces to substantiate this notion, the Prime Minister and Chancellor think they are broadly safe.

They are also confident no such evidence exists. As Osborne said in his evidence yesterday, why on Earth would the Tories have given responsibility for the bid to Vince Cable in the first place if they were engaged in some secret plan to stitch things up for News International? How could they have predicted that Cable would end up forfeiting his right to oversee the bid, thereby creating the opportunity to pass responsibility to Jeremy Hunt?

In other words, the Downing Street approach is to frame the allegations against them in terms that look like a crackpot conspiracy theory – the media/political equivalent of denying the moon landings. What they don’t fully appreciate, or at least what they can’t prevent, is the more general whiff of unsavoury cosiness with a corporate clan who clearly had privileged access to the corridors of power. On that front, the Downing Street rebuttal is that everyone was at it. Tony Blair and Gordon Brown played that game too and, say the Tories, sometimes played it even more vigorously.

Labour's riposte, reasonably enough, is that the current government has taken social intimacy with the Murdochs to a new level and that the quasi-judicial process around the BSkyB bid was specifically compromised, which is of a different order of offence.

But clearly some on the Labour side see the Leveson process as a way to get back at the Murdochs for what is seen as a wicked influence on political debate more generally in Britain. There is, on the left, an appetite for payback for what is seen as the long nurturaing of reactionary populism around issues such as welfare and immigration; and for the Sun’s treatment of Neil Kinnock.

Now it may be true that tabloids have coarsened political debate in Britain. It may also be true that there is a Tory bias in much of the print media and, indeed, that the Murdoch family has played a part in steering political discourse in Britain to the right. Leveson might decide that the process by which that happened was in some way dysfunctional but he cannot – or at least should not – be in the business of saying that one ideology was morally deserving of more or less influence than it got. He cannot, in other words, say what many on the Labour side feel, which is that the whole history of British politics since the 1980s was twisted against them and that Murdoch is in some way to blame. Leveson is not going to build Labour a time machine so they can go back and see what would have happened if Neil Kinnock had won the 1992 election.

So yes, the inquiry damages the government. It damages Cameron and Osborne. It raises all sorts of questions about the judgement of the Conservative leader - the choices he made with regard to the recruitment and defence of Andy Coulson [3]; the complacency over phone-hacking; the horse rides and Christmas picnics with Rebekah Brooks; the speedy unilateral exoneration of Jeremy Hunt, when plainly the Culture Secretary’s office was derelict in its duties to impartiality. No, on those points it doesn’t look good at all.

But it is important to disentangle different strands of outrage. There is the criminal behaviour and corruption that infected the journalistic culture at the News of the World and possibly other tabloid titles. There is the way that criminality penetrated the police force. There is the blurring of the boundary between a corporate interest and the decision-making process of government. Nowhere in that mix is it especially relevant that the Sun or other Murdoch titles gave Labour a hard time when they were in opposition in the 80s and early 90s. Nowhere in the inquiry's final report will there be a section devoted to lifting the shroud of false consciousness that the Murdoch press is somehow supposed to have imposed on the British people to make them less receptive to social democracy. If Labour wants to win the country round on that front, Leveson isn't going to help.

Labour can score many political points against the government around Leveson, but they should all be about judgement and due process. Ideology is best be kept well out of it.