Oblique breakdown in a supersonic flat-plate boundary layer is investigated using Direct Numerical Simulations (DNS) and Parabolized Stability Equations (PSE). This paper constitutes an extension to our previous studies of the complete transition regime of oblique breakdown. In these studies, the flow was assumed to be symmetric in the spanwise direction. A new DNS has been performed where the symmetry condition was removed. This simulation demonstrates that the "classical" oblique breakdown mechanism initialized by two symmetric instability waves with equal disturbance amplitudes loses its symmetry late in the turbulent stage for a low-noise environment. Hence, for the streamwise extent of the computational domain in our studies, the symmetry condition is justified. Furthermore, new data from a longer time average of the original symmetric simulation of oblique breakdown (CASE 3) are discussed. These data verify that a converged time average is reached. The final part of the paper focuses on a comparison of PSE results obtained from NASA's LASTRAC code to the DNS results. This comparison corroborates that the nonlinear PSE approach can successfully predict transition onset and that despite the large amplitude forcing used to introduce the oblique mode disturbances in the DNS, the latter constitutes a generic reference case for oblique breakdown at Mach 3 and, therefore, can be used to validate reduced order models for the full transition zone.