There are two significant sources of skin oils. One is sebum which is produced by the sebaceous glands. Sebum is involved with the development of acne infections. This subject is covered on the Cystic Acne and Acne Vulgaris pages. Sebum can be dry and firm, causing plugs and infections or it can be fluid and spill out of the follicles on to the surface of the skin.
Oil is also produced by the Lamellar bodies in the skin and its function is to protect the skin, creating a moisture barrier that helps prevent the skin and the body from becoming dehydrated. People with highly active Lamellar body functions can thoroughly wash the skin to the point that it becomes dry, but within 2-3 hours is will be oily again. These lipid barrier function oils are not involved with the development of acne infections.
Some people with excessively oily skin have acne and some do not have acne, because Lamellar body oils are not involved with acne. Therefore, it is possible to have excessively oily skin that has no role in the development of acne. Some people with excessively oily skin produce sebum that is very dry and firm and creates follicular plugs such as whiteheads or blackheads and eventually promote acne infections. See the Acne & Essential Fatty Acids page for more information on the subject of dry sebum.