That statement is as true as it is misleading, since no one has claimed that it took only cartoons. But contrary to your very naive separation of propaganda and violence, it's common knowledge that the antisemitic propaganda of the Nazis played an indispensable part in making the Holocaust possible. Influencing public discourses is massively important for the success of any political movement, including the worst ones.
Btw, I'm in no way making comparisons between this current cartoon 'scandal' and der Stürmer or anything, I'm just picking this up at the point I've found it.
In this case it shouldn't, as it was posted with critical intention.