We have performed experimental and theoretical studies of double ionization of helium by 6 MeV proton impact using a recently developed tool, four-particle Dalitz plots [Schulz et al., J. Phys. B 22, 3091 (2007)] which enable the representation of multiple differential cross sections as a function of all four fragments in a single spectrum without loss of any part of the total cross section. As a result, the relative importance of the various interactions between the fragments can be studied in great detail. Comparisons of experimental data with theoretical first-order calculations and simulations for the higher-order (TS-2) process show that elastic scattering between the heavy particles is surprisingly strong. For a large fraction of collision events, the final-state electron momenta are small compared to the momenta of the heavy particles. Our results suggest that an uncorrelated double ionization mechanism, involving two independent interactions of the projectile with both electrons, is significantly more important than previously expected for such fast collisions.