Hey, a friend of mine and "co-admin" on the site found the issue!
Since I use the german translation I have to roughtly translate the following by myself.
Under preferences -> Theme integration, there is a button "show advanced preferences".
When u hit it, you'll see a dropdown menu where it was set to "-- Simple header & footer static saved in cache --".
If you change it to "Whole Site: Fall back to index.php" it behaves like an iFrame on a normal wp-site.
Not as beautiful, but, for me it works now.
It really wasn't a bug at all, so, sorry wp-u for the misunderstanding.
Reading really helps sometimes! =)