Israeli reporter Anat Kam – whose long period of house arrest has been subject to a stringent gagging order that has been lifted only today – was not arrested for doing her job as a journalist. She was arrested for stealing and passing on classified military documents. Not that that makes her case any less unjust.

The story goes that, as a conscript serving as a secretary in the office of Maj-Gen Yair Nave, former chief of central command, Kam came into possession of numerous classified documents as a result of the lackadaisical attitude of a superior officer. When she left the army, she left it with a disc that contained, according to the Shin Bet internal security service, more 2,000 copied documents. These she passed to a journalist, Uri Blau of Haaretz. But the leak seems to have been traced back to her.

This is not a story about freedom of speech. The reporter in question submitted every one of these stories to the IDF military censor before publication – and not a single one was blocked. And there is nothing unique or unethical about Israeli laws that make it an offence to possess classified documents.

But the desperate attempt by the Shin Bet to prevent reporting of Kam's case has highlighted a paranoid and increasingly ridiculous obsession with secrecy on the part of the Israeli establishment. What is worrying is the ease with which the police and security services can go to the courts and forbid the media to report any detail regarding ongoing investigations.

It's as if the Shin Bet had never heard of the internet. Mass-market daily Yediot Ahronoth ran an already-iconic page reprinting a foreign-media story (by New York Times reporter Judith Miller) with the censored lines "redacted" in black. A few days later, they supplied readers with the necessary English key-words so they could google the foreign reports.

Indeed, Israeli friends have been gossiping about this story for weeks now. When I Googled Anat Kam's name a fortnight ago, there were no more than two or three hits. Today, there are more than 200,000 – and she even gets her own Wikipedia entry. Well done with that gagging order, guys.

The disappointing truth is that the furore over the attempt to block publication of Kam's arrest is a diversion that has also allowed the Israeli media to neatly sidestep the real story that emerged from the documents – that supreme court rulings over targeted killings of Palestinians were disregarded – and make it one of press freedom.

Only a minority of Israelis will get worked up about assassinations of alleged Palestinian militants. But when it comes to a theoretical restriction of their own freedom of information, that's something guaranteed to enrage them. It may have become a tired old Zionist trope but Israel does have a spectacularly free press, with eye-wateringly lax libel laws, sub judice a concept virtually unknown, and public debate sometimes exhaustingly healthy.

Ironically, the gagging order on this story has been lifted just after another one was imposed, referring to a very high-profile former politician already being investigated on corruption charges (although given Israel's current political make-up, that hardly narrows it down much).

And what now for Kam? She seems destined to become a scapegoat for a crime that theoretically carries a sentence of up to 15 years in jail – although, in previous cases, has only amounted to a matter of months. This seems particularly unfair, especially when the IDF has got to be one of the most indiscreet armies in the world. Privates and generals alike routinely brief reporters, and leak like sieves, to the point where officers now routinely have their phone records checked.

There has been no suggestion that Kam asked for or received any payments for the documents, although the Shin Bet's chief now maintains that Kam's actions did endanger Israel's national security – despite the fact that, according to the editor of Haaretz, the IDF censor passed the stories it ran that are alleged to have relied on information supplied by Kam.

The heavy-handed way in which Israel's security apparatus has handled this fiasco encloses a larger tragedy. Israel likes to market itself as a country of innovation and original thinking and, indeed, it does have one of the highest rate of start-ups and patents per capita in the world. But it simultaneously doesn't seem capable of giving up on another national doctrine: that if you're found doing something wrong, carry on doing it – just with more force.