No! That isn't it! I just found it out... I made everything absolute correct, but... like said, I have a clean installation, so only the sample data is in the db. If you try to ad the sample customer to a new group, the error happens. If you create a new user account, there is not problem at all! I really got mad to search for a bug ... but this problem happens if you make it 1:1 to the install. Think there is somewhere a wrong query with the sample (first?) customer?
Now, it seems to work. The product overview shows up the "normal" price, not group price. At the product_info itself everything is okay. But tomorrow I will have a look at the bugfix in the thread here, maybe there is already a solution. But keep the problem above in mind...