A theoretical understanding of the transport properties of the Quark-Gluon Plasma, such as shear and bulk viscosities, is essential for interpreting relativistic heavy-ion phenomenology. Recently, we introduced eight new Kubo formulas in Ref.[1] by fully determining the analytic structure of the stress-energy tensor correlation functions in the small-frequency and small-wavenumber limits. Obtaining the full stress-energy tensor correlation functions in any interacting theory is a highly nontrivial task. In this work, we first calculate the stress-energy tensor response functions in the Anderson-Witting model of kinetic theory with a nonzero mass. We then verify that these response functions satisfy the required analytic conditions, and are fully consistent with the recently derived Kubo formulas of Ref.[1]. For most of the new Kubo formulas, the order of the limits is reversed compared to the usual thermodynamic limit. Hence, our work serves as a nontrivial check for the validity of the stress-energy tensor correlation functions obtained from the gravity-coupled kinetic theory as well as the validity of the new Kubo formulas.