Relative permeability is a tensorial property directly dependent on absolute permeability tensor which has been taking both symmetric and non-symmetric (full tensor) forms in the literature. Imposing symmetricity during upscaling absolute and effective phase permeabilities could alter both diagonal and off-diagonal terms of relative permeability tensors, specifically in naturally fractured reservoirs (NFRs) where the diagonal components of the permeability tensor could take values with different orders of magnitude. Utilizing a discrete fracture and matrix (DFM) modelling approach, in this paper, we quantify the effects of forcing the symmetricity on absolute permeability tensors on relative permeability tensors of fractured samples in different scales. We also determine the circumstances at which this change in methodology causes a huge difference in the diagonal components of relative permeability tensors.