By and large, the 'best' research institutes in Germany are not the universities, but Max Planck and institutes like Fraunhofer. They may be loosely affiliated with the universities, but the University faculty and the research faculty are not one and the same. Students getting a doctorate may have that doctorate minted by the affiliated university, but all real work actually happens at the research institute.

Students can get doctorates directly from German universities and research is done there, but it's just not organized like American universities. Prime prestige centers are research institutes and they're spread around the country.