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.
By the letter, the situation might be better. But I don't think that in effect it is so much better.
How could one say, that something is "offensichtlich" (apparently) not usable in the business of the company. With any bigger company and when you take the software business and you program something for your own, you are caught. Which type of software related invention would "apparently" not be usable for (e.g.) Microsoft?
I have also spoken with German lawyers about that topic and what they told me, was not so rosy.
What is meant by "fair" compensation? I doubt very much, that this is regulated in detail and in effect the compensation will be what your employer says. For employee-inventions you also get some compensation ... and that should be fair too, I guess? But it is not, what I know. The compensation that regularly is given to the inventors inside a company get a fraction of the patent filing costs (in the US and also counting lawyer costs). I doubt that that could be counted as "fair", when the lawyers get more from the invention than the inventors.
(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.