Dear Leenie,
Why does the complexion clear up, too? Well, there are many schools of thought on that.

1) Daikon. If daikon is used, its property is to cancel out or get rid of fat-type of stagnations. Acne is just fat. You may even try applying daikon directly to your face! Slice a very thin slice of the raw daikon root and apply on blemishes with strategic bandaids overnight for several days. Even try this with warts.
2) Yin and yang. Acne is fat, and is yin (expansive) compared to a yang (contractive) item such as the root of daikon or its dried (yang) leaves, or salty, deepwater vegetable such as arame, or just salt. The yin of acne fat is canceled by the yang of any of these yang items: root of daikon, dried leaves of daikon, sea veg arame, or salt.
3) Skin 1. The skin acts like a third kidney, expelling toxins for us. The uterine area is part of that system -- the KD/BL or kidney/bladder/reproductive system. So when you clean one, you clean all! When you take a daikon hip bath, you are cleaning up the kidney/bladder/reproductive system. And since the skin acts like a third kidney, it benefits as well.
4) Skin 2. This idea takes more consideration. The skin is also thought of as an extension of the lungs and even remotely, the alimentary canal. Think about it: your nose is open, breathing back and forth, and if you open your mouth to breathe (and eat), you also take in air (and food). So whatever goes in, must go out. For example, fats have been eaten in the past, and perhaps in the last 1-3 months. They must come out. So one can choose to do many things to draw them out: either with direct compresses (the daikon slices), or by eating well (grate a tablespoon of raw daikon root with oil sautes, tempura, fish, oily foods), or by daikon hip baths. Why do the hip baths work here? Two reasons: One, Daikon & LU/LI: daikon is related to the LU/LI or lung/large intestine/brain area, and the large intestine gets a little bath, too, when you do a daikon hip bath, because it's located down there next to the uterus. So other areas benefit from that bath, such as the lungs, brain, and as an extension of the lungs -- the skin. Two, yin/yang: the top of the body, where acne is usually located, is considered more yin than the lower part of the body. When you want to stop the yin of acne (it's fat, and it's on top of body), you apply yang (dried daikon leaves or arame, or salt), to lower part of body (yang). It "pulls" the yin downward and helps to eliminate it properly through the bloodstream.

Many benefits, seen many ways. Try some of these remedies and see which work best for you.

Warmly,