Well, your assumption is just wrong. Please read different "Promotionsordnungen" of different universities (they differ slightly), but usually you'll have to finish your medical exams and afterwards you might do your Dr. med.. May require a minimum period of two years for the dissertation.
Yes, sometimes students are staring the required research work during their studies, but this led to the poor reputation of a "Dr. med." compared to the other "Dr." flavours. And yes, often the quality of a medical dissertation is compareable to a good Masters thesis. Nonetheless, formally the "Dr." is one step on top of the "Master".
Nonetheless, you can do clinical research, but you are not allowed to apply as PI for some (many) funding schemes. But of course you can work in research! BTW: I never heard of a fresh medical doctor who succeeded in applying grants on his / her own - so in practice it makes no difference.
I would suggest looking for a position which allows you to obtain a doctoral degree - in your case you might even be able to get two (one Dr. med., one Dr. rer nat (or similar)) depending on whether you are building upon your medical or your neuroscience background. But it will take at least two years.