Linear energy scaling laws connect the kinetic and thermodynamic parameters of key elementary steps for heterogeneously catalyzed reactions over defined active sites on open surfaces. Such scaling laws provide a framework for a rapid computational activity screening of families of catalysts, but they also effectively impose a fundamental limit on the theoretically attainable activity. Understanding the limits of applicability of the linear scaling laws is therefore crucial for the development of predictive models in catalysis. In this work, we computationally investigate the role of secondary effects of the active site environment on the reactivity of defined Fe complexes in ZSM-5 zeolite toward methane oxofunctionalization. The computed C-H activation barriers over Fe-sites at different locations inside the zeolite pores generally follow the associated reaction enthalpies and the hydrogen affinities of the active site, reflecting the O-H bond strength. Nevertheless, despite the close similarity of the geometries and intrinsic reactivities of the considered active complexes, substantial deviations from these linear scaling relations are apparent from the DFT calculations. We identify three major factors behind these deviations, namely, (1) confinement effects due to the zeolite micropores, (2) coordinative flexibility, and (3) multifunctionality of the active site. The latter two phenomena impact the mechanism of the catalytic reaction by providing a cooperative reaction channel for the substrate activation or by enabling the stabilization of the intrazeolite complex along the reaction path. These computational findings point to the need for the formulation of multidimensional property-Activity relationships accounting for both the intrinsic chemistry of the reactive ensembles and secondary effects due to their environmental and dynamic characteristics.