I have wondered about this for a long time. I'm almost positive that if I didn't have oily skin, I wouldn't have acne problems anymore. BUT, from what I've read over the years, it is not the oil itself that causes the acne, it is the bacteria and dead skin along with oil that clogs a pore. The oil definitely contributes to causing acne, but by itself it doesn't. For example, my skin doesn't shed/get rid of dead skin properly. I know this because of how flaky it is; so dead skin particles + the oil is what clogs the hair follicles on my face, leading to acne.

Also, I have a friend who's skin is a little oily, but he rarelyhas any acne problems and does everything you mentioned above.