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We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr₂O₄ in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in MgCr₂O₄ are faithfully represented in the entire Brillouin zone by a theory of magnon excitations propagating in a highly-correlated paramagnetic background. Our results also suggest that MgCr₂O₄ is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, what has implications for the magneto-structural phase transition observed at low temperature in this material.