This paper discusses the problem of a spherical anisotropic scatterer exposed to a uniform electrostatic field. It has been common in previous literature to treat this problem similar to the case of isotropic sphere for which it is known that the internal field is uniform throughout the volume of the sphere. In this paper, a proof is given for the uniformity of the field inside the anisotropic sphere, which (to the authors' knowledge) has not been proven before. This result gives rigorous justification to those analyses in which the polarizability matrices of anisotropic inclusions are determined and the effective material parameters of anisotropic mixtures are calculated. In the present article, the proof is also generalized for bianisotropic spheres within electromagnetostatic field.