It isn't anything to do with sugar, soy naturally has phytoestrogens in it. It can aggravate acne in some people (myself included if I eat a lot of tofu or drink too much soymilk) because it can mess with your hormone levels. However, it has also been cited to help acne for some as well, it really depends on what type of acne you have and if hormones play a role it in or not. Birth control that was supposed to help acne never worked for me, everyone is different. The benefits of soy are really exaggerated though, and there have been potential dangers with consuming too much as well, like breast cancer.
This is actually the same reason that dairy products can wreck havoc on certain people's skin, but due to a different hormone. Milk has androgen hormones in it, which has a definite link to acne. While soy will have mixed results in how it effects your skin, I think you'd be hard pressed to find someone who needed more testosterone for their acne. (Testosterone is an androgen hormone, and why steroid users get bad skin).
Cutting out dairy cleared up my face 90%+ I used to consume quite a lot of it, I cut it out before making other dietary changes so I am certain it was the dairy. Dr. Bronner's soap instead of the usual chemical crap also helped. I cleared up in about 2 weeks or so. Right now I have 1 new zit on my jawline but thats pretty spectacular for me. I am now also meat free, and refined, processed food free, so no wheat or sugar. It basically translates to a vegan diet, with limited soy. (I made these changes specifically to clear up my skin). It is not too difficult for me because I was strict vegetarian before and love to cook. I use hemp milk, I like the taste and it's better for you. While my face is great now, my bacne is still being stubborn. I'm not even sure if its bacne anymore, but there has been slight improvements.
For reference my acne was mild on my face but moderate/very painful on my jawline. My bacne is still moderate but lately has been a bit less painful and scarring, but I don't want to jinx myself!
I take vitamins when I can remember, mostly zinc and b vitamins, probiotics too. I think I will try to take them regularly and add some vitamin c and selenium. I'll be sure to update with any improvements. It's nice to see more people making the link to possibly dietary causes and trying a natural approach. Not that I care if you take accutane or something, it's just encouraging seeing I'm not alone in my hippie endeavors!
Good luck everyone!