Injection-induced seismicity (IIS) typically occurs when pressure diffuses from a sedimentary target formation down into fractured and faulted, low-permeability, critically-stressed basement rock. Previous studies of IIS have used basin-scale models of pressure diffusion that rely on an equivalent porous medium (EPM) approach to assign hydraulic diffusivity and a triggering pressure (TP) criteria for seismic initiation. We show that these models employed unrealistically-large values of hydraulic diffusivity, usually by neglecting the compressibility of the fractures in the specific storage coefficient, to result in pressure diffusion to seismogenic depths (≥2 km into the basement). The EPM-TP approach does not explicitly represent the mechanical and hydrologic behavior of fractures and faults, and it fails to explain why relatively few disposal wells are associated with IIS. We develop a parallelized, partially-coupled, hydro-mechanical, discrete fracture network and matrix model (DFNM) model with thousands of fractures and the capability to calculate Mohr-Coulomb (MC) failure to indicate seismicity and alter hydraulic diffusivity. In consistent comparisons, DFNM-MC simulations allow for deeper, more heterogeneous pressure diffusion than EPM-TP simulations, and they do not need to employ unrealistic diffusivity values to result in pressure diffusion to seismogenic depths. A sensitivity analysis shows that small deviations in fault orientation (≤2 degrees from optimal) and fracture network density outside an intermediate range can drastically decrease the likelihood of IIS, potentially explaining why only a small fraction of disposal wells are associated with IIS. The EPM-TP approach is unsuitable to investigate IIS, but the DFNM-MC approach offers a promising, nuanced approach for further study.