Actually, go read the law (ArbnErfG, § 18 Mitteilungspflicht, Satz (3)) says otherwise:

(3) Eine Verpflichtung zur Mitteilung freier Erfindungen besteht nicht, wenn die Erfindung offensichtlich im Arbeitsbereich des Betriebes des Arbeitgebers nicht verwendbar ist.

The law also stipulates that for any invention or major improvement, even for the ones that you do during your work time that your employer wishes to keep the rights for, you're entitled to a fair compensation. So yes, if you invent something that is related to your employers business, the employer gets the first right. But I do think that the situation is much better - you at least get compensation.