The claim of barbarism and violence is actually based on Adorno's very deep connection to what he continually refers to as "Auschwitz", to the point where he'll even describe the world as a post-Auschwitz world. In his lectures (published 1964) he also mentions the atom bomb. As a German Jewish emigrant to the U.S., the question of Nazi Germany had a huge effect on him and his beliefs - in particular this Hegelian notion of history moving to ever higher stages of freedom in a linear fashion. The existence of the Nazis at such a scale could not be explained as simply an aberration - the Frankfurt School was born out of this struggle to find out what went wrong and what is going wrong with both Hegel's thesis and Marx's thesis.