Breakouts are occour under the skin, from the oils in your pores. It is impossible to eat fat and have that fat wind up in your pores. Androgens can cause an overproduction of the pore oil sebum. Androgens cause break outs, not dietary fat. If you find you are breaking out more on atkins, it is probably because your body is adjusting to new hormonal levels as insulin production is being lowered/normalized. It may take awhile for every other hormone to adjust, so for awhile you may have to live temporarily with elevated androgen levels.

For me personally, I had terrible acne BEFORE starting atkins. It was like a miracle, once I began atkins my face cleared up and I never get blemishes now. I now know this is because I was producing WAAAY too much insulin and my testosterone levels were also too high from it. I probably had undiagnosed pcos to be honest, since I had all symptoms of an overproduction of insulin and testosterone.
Although, I do find my skin to be very dry now (a problem I never had before). I attribute this to estrogen dominance, as I am breaking down a lot of stored fat which is artifically elevating my estrogen levels. Once I lose the weight and progress into maintenence I figure this will go away.

Just stick it out a few weeks, and I gaurentee once your body adjusts you won't have any blemishes anymore. Blemishes are caused by hormones, not fat. In fact, blemishes are caused more by refined carbs than they are fat since refined carbs muck up our hormones!