The Leveson Inquiry into the press came to life yesterday as Sally Dowler re-lived the moment, eight years ago, when she was given false hope that her missing daughter, Milly, might be alive. She told her husband: "She's picked up her voicemails, Bob. She's alive!" That moment will stand for a long time as a shocking low point in the sometimes murky history of the British press.

After the Dowlers came the actor Hugh Grant, who has also conducted a very effective campaign to expose the abusive behaviour of parts of our profession. Other witnesses will include the comic actor Steve Coogan, and the former head of Formula One Max Mosley – two other vocal critics of the press. They all have stories to tell that show the tabloid papers, particularly the now defunct News of the World, in an appalling light. But there is a danger that the inquiry will impute too much from these extreme examples.

The Dowler case is in a class of its own. There are no circumstances under which people who have been dragged under the spotlight as victims of a sensational crime should have their privacy deliberately invaded. Anyone who does what was done to the Dowler family deserves to end up in prison.

But the complaints of celebrities such as Hugh Grant have to be treated with more caution. Mr Grant chose to enter a profession which would make him a public figure. He chose to be an object of interest, but complained when press interest in him took an unpleasant turn. It is not a straightforward question how much celebrities like Mr Grant should be able to control what is written about them. There is a danger that in seeking to protect individual privacy, the Leveson Inquiry will restrict the public's right to know whether their celebrities are what they appear to be.

Among the famous and the powerful there will always be a minority who are unpleasant, hypocritical or actually corrupt, who would love to be able to command the kind of protection from media scrutiny that Mr Grant demands, and to which the innocent Dowlers were obviously entitled. The Leveson Inquiry should not lose sight of that.