We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr_{2}O_{4} in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all of the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr_{2}O_{4} are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly correlated paramagnetic background. Our results also suggest that MgCr_{2}O_{4} is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magnetostructural phase transition in MgCr_{2}O_{4}.
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