Carbon-based, molecular semiconductors offer several attractive attributes for spintronics, such as exceptionally weak spin-orbit coupling and compatibility with bottom-up nanofabrication. In spite of the promising properties of organic spin valves, however, the physical mechanisms governing spin-polarized conduction remain poorly understood. An experimental study of C60-based spin valves is presented and their behavior is modeled with spin-polarized tunneling via multiple intermediate states with a Gaussian energy distribution. It is shown that, analogous to conductivity mismatch in the diffusive regime, the magnetoresistance decreases with the number of intermediate tunnel steps, regardless of the value of the spin lifetime. This mechanism has been largely overlooked in previous studies of organic spin valves. In addition, using measurements of the temperature and bias dependence of the magnetoresistance, inhomogeneous magnetostatic fields resulting from interfacial roughness are identified as a source for spin relaxation and dephasing. These findings constitute a comprehensive understanding of the processes underlying spin-polarized transport in these structures and shed new light on previous studies of organic spin valves.