This is an older topic, but I just had to add my experience. Coffee absolutely can cause acne. When I was in my teens i had fairly severe acne. I thought it was processed food causing the acne. I would try very hard not to eat any of that stuff but if I made a mistake one day and had a cookie or something acne would blossom all over my face. And not just tiny red bumps, but big ones, medium sized ones... I was big coffee lover during those years and I'd drink three mugs a day religously.
Then one day I came down with Salmonella and I didn't feel like even drinking anything that day (so no coffee). I noticed the next morning that my skin looked quite a bit better and not so red. After not being able to eat or drink the next day, my skin was really showing an improvement like never before. I suspected caffeine and so I totally cut it out and I experimented by taking sweets at the same time.
What happened was my skin began to heal. New zits stopped coming up and old zits were healing and my face was looking whiter and actually started to clear up. I can eat whatever I want now, as long as I don't consume any caffeine. When I first made the discovery I went around for a couple of days eating all the sweets I could find. At first I only had to stop drinking coffee for my face to clear up, but then my system got more sensitive to smaller amounts of caffeine and I've had to stop drinking regular tea and green tea. I can still have some caffeine in a very trace amount, like a square of chocolate.
That being said, if you do have acne, when you eat healthy and avoid processed food and especially sugar, your skin seems to heal faster, especially from post-inflammatory hyper-pigmentation. That's because fruits and vegetables have vitamins and minerals that affect your skin positively. Drinking lots of water makes a lot of difference too. But it's nice to be able to have a piece of cake or ice cream once in awhile. Occasionally I still have a cup of coffee and on those days I make sure to completely cut out the junk food.
I can't scientifically explain this problem with caffeine. I want to add that I had cystic, hormonal acne. I had been diagnosed with it by my doctor. It wasn't just a rash from an allergic reaction. Anyway, hope this helps.