It's all about the keycaps. Cherry has the lowest (I really like them). Signature plastics is next. The highest is "OEM profile, which is used by filco, WASD, and others.
So if you put a cherry DS set on anything, it'll be pretty low.
I have a cherry DS set on my WASD. I think it has acceptable height above the frame, but this is just my preference. It looks similar to your picture.
You can do some things, like sticking spacers on your stems to raise the keycap height. If you raise them too much, they'll become wobbly, though.