He may not have ordered the killing of Anna Politkovskaya, but Putin has been unable to combat the chaos that caused it

More than once, I have listened to a Russian tell me the convoluted story of how a grandparent was killed on the personal orders of Stalin. Sometimes, I sensed they knew this was far-fetched, but this myth gave an explanation and a higher meaning to their relative's death.

When a journalist and Putin critic is killed in Russia (or London), the reaction is often the same from journalists. The immediate rush to judgment is that the "ex-KGB colonel" is somehow involved. It certainly makes a good story that is easy to understand and excites the emotions by personalising the perpetrator.

But I have never been truly convinced of Putin's involvement in a grand Kremlin plot to kill Anna Politkovskaya, a crime that finally reached court this week. When he said that she was "very minor", he was not so much denigrating her journalism as being callously honest – there would have been too many negatives from having her killed, not least the bad press abroad.

Under Putin, as under Yeltsin, the deaths of journalists have mainly been connected with the trouble in Chechnya and Ingushetia or the investigation of shady business deals and corruption. Just this week, a local Moscow journalist was badly beaten after providing critical coverage of the local authorities. The fact that the people who ordered Politkovskaya's killing (most likely someone she was investigating in Chechnya) have not been found does not mean that the Kremlin was behind it. It means that someone with enough power – control over guns or money – does not want the truth to get out.

Just as with Stalin, people have an impression of Putin as an all-powerful dictator who controls every aspect of his country. This impression is pushed by Russian and western media, as well as Putin himself and his allies. But it's a mirage. While we think of Putin as an dictator, directly responsible for the death of journalists, we miss the point. We need to get deeper inside what make Russia a country where this kind of thing can happen.

This is not to absolve Putin of responsibility for what happens in Russia. His leadership has failed to bring about a form of governance and society where the truth will out and punishment awaits the real perpetrators, and not just the small fish, as in this trial. Putin did not create this problem, but he has utterly failed to solve it.

Rather ironically, Putin's biggest failure turns out to be his inability to bring order to a country still controlled at a local and national level by the power of guns and money. The much-vaunted stability that he brought to the country has been largely financial, fuelled by petrodollars, and it now appears to be unravelling as the price of oil plunges.