Hubertus Andrae, the Munich chief of police, shook his head and let out a sigh when asked about thegunman’s politics. Not even a day had passed since a shooting rampage on his patch of southern Germany had left nine people dead, most of them teenagers. But the chief already felt confident enough in the investigation todismiss any links to Islamicextremism. The young killer, a dual citizen of Germany and Iran who was born and raised in Munich, had an “obsession” with indiscriminate violence, Andrae said, and apparently decided to “run amok” outside the city’s biggest shopping mall.

Still, it seemed a bit early to call the case closed. When we spoke at police headquarters on Saturday afternoon, the chief conceded that his officers had not yet analyzed all the gunman’s computers and social media accounts. Nor had investigators been able to question all the witnesses of the rampage, one of whom told CNN that the gunman shouted Allahu Akbar – “God is great” – while firing his Glock into a crowd of people near a McDonald’s restaurant. Pressed on this point, Andrae was dismissive. “Even if he would have said this, it would not automatically indicate anything,” he told me. “Not everyone who uses this saying, which is now famous around the world, is automatically linked to ISIS.”

Clearly not. That phrase is an everyday expression of faith for many of the world’s 1.6 billion Muslims. But shouting it during a shooting spree is also a hallmark of Islamist violence, one of the few reliable signs that investigators have at a time when the very idea of what is terrorism and what is crime has become increasingly hard to pin down. That is the reality ISIS has helped create. In their propaganda, the group’s leaders have been happy to claim responsibility for any atrocity their death cult inspires, even when the perpetrator has had no discernible ties to the group other than the vague and virtual relationship often referred to as “self-radicalization.”

Germany has learned that lesson. On July 18, a young Muslim asylum seeker armed with an ax and a knife attacked a group of passengers on a train in the town of Würzburg, leaving five people gravely injured. In a video posted online, that attacker had pledged allegiance to ISIS, which in turn took responsibility for the bloodshed he caused, calling the 17-year-old axman a “soldier” of its self-declared caliphate. At least on an ideological level, the link to ISIS seemed as plain as it could be.

But in that case, too, German authorities were careful not to draw too clear a line between the perpetrator and any kind of Islamic extremism. Even after confirming the authenticity of the Würzburg attacker’s suicide video—in which he pledges allegiance to ISIS and vows to kill “non-believers”—Germany’s top police official would not qualify the attack as an act of terrorism. “It is in a grey area between a rampage and terrorism,” said Interior Minister Thomas de Maizière, using the German term Amoklauf—literally, “running amok”—itself a borrow from a Malay word, which normally refers to mass shootings and other attacks with no clear political motive.

There could be many reasons for this abundance of caution on the part of German authorities. For one thing, they may not want to play into the hands of ISIS, which has sought to convince the world that its reach is limitless exactly because it can inspire attacks without explicitly directing them. “We tend to focus on their messianic vision of killing the infidels, but in reality ISIS leaders are students of geopolitics,” says Michael Weiss, co-author of ISIS: Inside the Army of Terror. “The logic is dialectical: encourage or ‘inspire’ jihadi attacks; precipitate anti-Muslim backlash (which can take the form of simply everyone assuming that a mass shooting must be Islamist, even when it isn’t) and wait for the West to cannibalize itself.”