The contributions to the cross sections of intermediate energy two-nucleon knockout reactions from events in which one nucleon is removed by the stripping (inelastic breakup) mechanism and a second by the diffraction (elastic breakup) mechanism are discussed. The small additional contributions from two-nucleon diffraction events are also estimated. The approach used combines the eikonal reaction and shell model structure theory frameworks. For reactions involving the removal of two well-bound like nucleons, at incident energies of order 100 MeV per nucleon, the additional cross sections are shown to be of approximately the same size as those from events in which both nucleons are stripped in inelastic interactions. These more complete dynamical calculations now permit a quantitative comparison of the theoretical cross sections with recent partial cross-section measurements of the two-neutron (two-proton) removal reactions from neutron-deficient (neutron-rich) nuclei. As has been observed in both nuclear- and electron-induced single-nucleon knockout reaction analyses, the theoretical two-nucleon knockout cross sections overestimate the measured values, requiring a suppression of the two nucleon shell-model transition strengths. The deduced two-nucleon suppression factors, R_s(2N), are consistent with a value of 0.5 for each of the five reactions considered.