We study the drainage of a near-theta solvent through densely grafted polymer layers and compare to recent notions that these layers display little permeability to solvent flow at surface separations less than a "hydrodynamic thickness." The solvent is trans-decalin (a near-theta solvent at the experimental temperature of 24 degrees C). The polymer is polystyrene (PS) end-attached to two opposed mica surfaces via the selective adsorption of the polyvinylpyridine (PVP) block of a PS-PVP diblock copolymer. The experimental probe was a surface forces apparatus modified to apply small-amplitude oscillatory displacements in the normal direction. Out-of-phase responses reflected viscous flow of solvent alone-the PS chains did not appear to contribute to dissipation over the oscillation frequencies studied. The value of the hydrodynamic thickness (R-H) was less than the coil thickness (L-o) measured independently from the onset of surface-surface interactions in the force-distance profile, implying significant penetration of the velocity field into the polymer layer. As the surface-surface separation was reduced from 3L(o) to 0.3L(o), the apparent hydrodynamic thickness (R-H*) decreased monotonically to values R-H*much less than R-H. Physically, this indicates that the "slip plane" moved progressively closer to the solid surfaces with decreasing surface-surface separation. This was accompanied by augmentation of the effective viscosity by a factor of up to approximately 5, indicating somewhat diminished permeability of solvent through the overlapping polymer layers. Similar results hold for the flow through surface-anchored polymers in a good solvent. It is interesting to note the strong stretching of densely end-grafted polymers in a theta solvent.