Discoveries of room-temperature ferromagnetism (RTFM) in semiconductors hold great promise in future spintronics technologies. Unfortunately, this ferromagnetism remains poorly understood and the debate concerning the nature, carrier-mediated versus defect-mediated, of this ferromagnetism in semiconducting oxides is still open. Here, by using X-ray absorption (XAS) and X-ray magnetic circular dichroism (XMCD), it is demonstrated that the oxygen ions have a ferromagnetic response in different ZnO-based compounds showing RTFM behavior: ZnO nanoparticles capped with organic molecules and ZnO/ZnS heterostructures. These results demonstrate the intrinsic occurrence of RTFM in these systems, and point out that it is not related to the metallic cation but it relays on the conduction band of the semiconductor.