I think I found the answer. I had chosen the option "No stretch" for "Image stretch". The problem was the german translation. If you chose "keep aspect", than the images are streched down in the right proportion. The english description "keep aspect" makes a lot more sense.
If you chose "no stretch", than the whole textobject will be scaled down at a lower resolution, but the background image will stay in the original resolution. The result of this will be, that the image will be cut at a smaller resolution.