Thank you for your quick answers. LostKobrakai was right, it had nothing to do with permission but was a multilanguage problem.
I was under the impression, that the default language, being english, is somehow carved in stone. Because I wanted german to be my default language, I therefore installed german, made it hidden and locked, so that it would not appear in pages. The trouble started as I configured the guest user to use that hidden language.
Now I have deleted german as a separate language and dropped the german translation files onto the default language. That seems to work so far.