In texturally equilibrated porous media the pore geometry evolves to minimize the energy of the liquid-solid interfaces, while maintaining the dihedral angle θ at solid-solid-liquid contact lines. We present computations of three-dimensional texturally equilibrated pore networks using a level-set method. Our results show that the grain boundaries with the smallest area can be fully wetted by the pore fluid even for θ > 0. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Even small anisotropy in the fabric of the porous medium allows the wetting of these faces at very low porosities, ϕ<3%. Percolation and orientation of the wetted faces relative to the anisotropy of the fabric are controlled by θ. The wetted grain boundaries are perpendicular to the direction of stretching for θ > 60° and the pores do not percolate for any investigated ϕ. For θ < 60°, in contrast, the grain boundaries parallel to the direction of stretching are wetted and a percolating pore network forms for all ϕ investigated. At low θ even small anisotropy in the fabric induces large anisotropy in the permeability, due to the concentration of liquid on the grain boundaries and faces.