We develop a theory of angular-dependent magnetoresistance (ADMR) in metallic altermagnets coupled to ferromagnetic insulators and establish criteria that distinguish them from conventional compensated magnets with spin-orbit coupling. We show that, once its full set of angular dependencies is established, the spin-splitter magnetoresistance (SSMR)-- recently reported in the bilayer geometry of H. Chen et al. [Adv. Mater. 37, 2507764 (2025)] – would constitute a smoking-gun signature of collinear d-wave altermagnetism in metallic systems. Although SSMR has been regarded as a close analogue of spin Hall magnetoresistance (SMR), we demonstrate that the two differ qualitatively in three key respects: SSMR depends solely on the relative orientation between the ferromagnetic magnetization and the altermagnetic Néel vector, yields a longitudinal ADMR response of opposite sign, and features a direct proportionality between longitudinal and transverse ADMR signals, absent in SMR. Building on these distinctions, we further show that the full angular dependence of the SSMR provides a practical recipe to extract the direction of the Néel vector from customary magnetoresistance measurements. These results provide a clear route to unambiguously identify altermagnets in transport.