Yep, I stand corrected.

http://de.wikipedia.org/wiki/Mitf%C3%BChrpflicht

You have to have one, but you don't have to have it on you at all times, with some exceptions - for example, when carrying a (legal) weapon and whilst at work in specific industries (hospitality and construction are mentioned).

I believe,though, that if you don't have it on you and the police want to see it they can insist on accompanying you home. ("Didn't have to pay for a taxi home from the disco last night. Police gave me a lift")