Multiple unsteady-state methodologies have been developed to estimate permeability at the laboratory scale, but with limited success in the assessment of ultra-low (i.e., nano-Darcy level) permeabilities. As industrial attention grew for lithologies demonstrating such low permeabilities, most notably as source rocks for unconventional oil and gas recovery and as geologic confining zones for deep subsurface waste containment, variants of the pressure-pulse-decay methodology were designed to decrease test times by enhancing the surface area accessible to the pulse and allowing fluid ingress along multiple directions. Despite the increasingly complex flow field induced by such approaches, the most widely used models today assume sample materials to have uniform permeabilities. In this study, we investigate the effect of assuming an isotropic fabric for materials that show strong anisotropic behavior, particularly layered media like shales. Assuming these sample materials are composed of a very strong anisotropic fabric, we describe multiple forward models to simulate the anticipated pressure responses for pulse-decay measurements performed on fractured cylindrical samples and crushed fragments by negating flow perpendicular to bedding. Then, using the inverse modeling analyses available through iTOUGH2, we fit the various models to synthetic data and compare their results. From this, we show how the assumption of an isotropic fabric could lead to bulk permeability estimates with limited physical significance. We also suggest potential strategies to account for anisotropy in the experimental design through the data-inversion framework.