Absolute cross sections for collisional depopulation of 2.5-40 keV u^-1 Rydberg hydrogen atoms have been measured in Ar, N₂, CO₂ and SF₆. The data establish unambiguously that both the Rydberg electron and the proton core scatter quasi-freely. This result confirms Matsuzawa's (1980) theoretical description of fast collisions of Rydberg atoms with neutrals. Consequently, under certain conditions the dominant Rydberg atom depopulation mechanism is that of core collisions and the total scattering cross section of a fast Rydberg atom reaches a natural limit, independent of the principal quantum number n, given by the independent-particle model.