David Cameron sees the Leveson inquiry as an "opportunity" to reassess the relationship between the media and politicians. But his desperate political positioning to save Jeremy Hunt only underlines the likelihood that nothing is likely to change.

The situation, as the prime minister made very plain on a TV sofa this morning, is very simple. It doesn't matter that Lord Justice Leveson is refusing to have anything to do with the question of whether ministers are behaving badly. What matters is that Hunt is going to answer questions, under oath, in front of a judge.

He'll be questioned about the inappropriate communications which emanated from his office with News Corporation during its attempt to takeover broadcaster BSkyB. How much did he know about the behaviour of his special adviser, Adam Smith, whose actions he condemned so uncompromisingly in the Commons last Wednesday? If it can be shown that he knew exactly what Smith was up to, he'll have to go.

The problem is one of process. No 10 found itself in a rather awkward position when it became obvious that Leveson wouldn't have anything to do with this very political affair. He wasn't even prepared to play ball and let Hunt appear before the inquiry ahead of schedule. What was Downing Street to do? Clearly, further scrutiny of Hunt's behaviour was required. An internal government inquiry risked being dismissed as a whitewash.

No 10's solution, it emerged this weekend, is to just let the Leveson inquiry get on with it. Here's Cameron explaining this rationale on BBC1's The Andrew Marr Show this morning: "The inquiry's underway. Jeremy Hunt is preparing evidence for that inquiry, evidence they will give under oath. If information arises that paints a different picture from the one we've heard, then obviously I know my responsibilities towards the ministerial code and I would act."

It is Cameron, not Leveson, who will deliver the final verdict on Hunt's behaviour – a state of affairs which is not going unquestioned in Westminster. The prime minister is about as obviously biased as Rupert Murdoch would be were he chairing the Leveson inquiry, those calling for Hunt's scalp say. Yes, David Cameron will do his duty and fire Hunt if it becomes clear he has no choice. But if Hunt's evidence is equivocal or inconclusive, Cameron will be able to save the skin of his culture secretary. A process open to question, that much is sure.

No 10's gamesmanship paves the way for a public trial of Hunt. For if public opinion about his conduct will be the decisive factor in determining whether Cameron feels he has no choice but to drop Hunt, it is the media which will play a leading role. The interpretations of journalists and editors following Hunt's evidence will collectively decide if he gets to stay or is shown the door.

This underlines how important the media are to politicians. It is in exactly these sorts of battles where good past relationships between politicians and the powerful media figures controlling the headlines behind the scenes become vital. That is never going to change: politicians will always be looking to increase their chances when the going gets tough.

"The problem of the relationship between media and politics has been going on for a long time," Cameron said earlier today. "We've got the opportunity to get it to a much, much better place."

How, exactly, that will be achieved remains to be seen. The fundamentals of their relationship are not going to be transformed by the Leveson inquiry, or by what comes afterwards. As Cameron's manoeuvrings to increase the chances of saving Hunt's skin show.