Observations of T Tauri stars and young brown dwarfs suggest that the accretion rates of their disks scale strongly with the central stellar mass, approximately M˙~M2*. No dependence of accretion rate on stellar mass is predicted by the simplest version of the Gammie layered disk model, in which nonthermal ionization of upper disk layers allows accretion to occur via the magnetorotational instability. We show that a minor modification of Gammie's model to include heating by irradiation from the central star yields a modest dependence of M˙ on the mass of the central star. A purely viscous disk model could provide a strong dependence of accretion rate on stellar mass if the initial disk radius (before much viscous evolution has occurred) has a strong dependence on stellar mass. However, it is far from clear that at least the most massive pre-main-sequence disks can be totally magnetically activated by X-rays or cosmic rays. We suggest that a combination of effects are responsible for the observed dependence, with the lowest mass stars having the lowest mass disks, which can be thoroughly magnetically active, while the higher mass stars have higher mass disks that have layered accretion and relatively inactive or ``dead'' central zones at some radii. In such dead zones, we suggest that gravitational instabilities may play a role in allowing accretion to proceed. In this connection, we emphasize the uncertainty in disk masses derived from dust emission and argue that T Tauri disk masses have been systematically underestimated by conventional analyses. Further study of accretion rates, especially in the lowest mass stars, would help to clarify the mechanisms of accretion in T Tauri stars.