We report DFT+U results on oxygen adsorption and extraction characteristics obtained for a realistic model of a strong metal-support interaction catalyst, exemplified by a Pt(111)-supported FeOx ultra-thin film. Derived from recent experimental results, the model enables a coherent analysis of the activity towards oxygen at a large variety of sites, which range from FeO and FeO2 oxide terraces to different oxide-metal and oxide-oxide boundaries. We show that the trends in calculated adsorption and desorption energetics are to a large extent specific to the small thickness of the supported oxides and are mainly driven by electron exchange with the underlying metal substrate. The thorough mapping of the activity of different local surface environments enables the identification of the sites that are most likely responsible for the observed low-temperature activity of FeOx/Pt films in CO oxidation. Beyond the oxide-metal boundaries known for their higher activity than the separate materials, we find that the sites at boundaries between the coexisting oxide phases of different compositions can easily adsorb and release oxygen.