The V_1−xMo_xO₂ phase diagram has high structural and electronic complexity that is driven by strong, short-range correlations that compete with the long-range rutile crystal structure. The substitution regime near 50% Mo occupancy is no exception, but there has so far been no significant progress in determining the actual structure. Reported here is a combined study using single crystal X-ray diffraction, powder X-ray diffraction, and representational analysis to examine both the local and crystallographically averaged atomic structures simultaneously near x = 0.50. Between about x = 0.50 and 0.60, the average structure of V_1−xMo_xO₂ is the parent rutile phase, but the local symmetry is broken by atomic displacements that are best described using the orthorhombic subgroup Fmmm. This model is locally similar to the two-dimensionally ordered 2D-M2 phase recently reported in the compositional range 0.19 ≤ x ≤ 0.30, except the correlation length is much shorter in the 2D plane, and longer in the frustrated one, making it more isotropic. This work also extends the 2D-M2 phase regime up to x = 0.43, and suggests that the local-Fmmm phase observed here can be seen as the end result of the continued suppression of the 2D-M2 phase through enhanced geometric frustration between the intrinsic order parameters. This suggests that other doped-rutile phases with elusive structures may also be dominated by similar short-range correlations that are hidden in the diffuse scattering.