We report 491 new near-infrared spectroscopic measurements of 420 near-Earth objects (NEOs) collected on the NASA InfraRed Telescope Facility as part of the MIT-Hawaii NEO Spectroscopic Survey. These measurements were combined with previously published data from Binzel et al. and bias-corrected to derive the intrinsic compositional distribution of the overall NEO population, as well as of subpopulations coming from various escape routes (ERs) in the asteroid belt and beyond. The resulting distributions reflect well the overall compositional gradient of the asteroid belt, with decreasing fractions of silicate-rich (S- and Q-type) bodies and increasing fractions of carbonaceous (B-, C-, D- and P-type) bodies as a function of increasing ER distance from the Sun. The close compositional match between NEOs and their predicted source populations validates dynamical models used to identify ERs and argues against any strong composition change with size in the asteroid belt between ~5 km and ~100 m. A notable exception comes from the overabundance of D-type NEOs from the 5:2J and, to a lesser extend, the 3:1J and ν ₆ ERs, hinting at the presence of a large population of small D-type asteroids in the main belt. Alternatively, this excess may indicate preferential spectral evolution from D-type surfaces to C and P types as a consequence of space weathering, or point to the fact that D-type objects fragment more often than other spectral types in the NEO space. No further evidence for the existence of collisional families in the main belt, below the detection limit of current main-belt surveys, was found in this work.