Pimples and acne do not cause the face to become oily; rather, excess oil production (sebum) is a primary factor that contributes to the development of acne.
The claim gets the causal direction backwards. In dermatology, excess sebum production from the sebaceous glands contributes to the development of acne (along with hyperkeratinization and bacterial colonization), not the other way around. The retrieved literature (such as papers 8 and 9) describes increased sebum production as an underlying cause of acne.