"Checking left and right separately does nothing to determine if you are having a phase issue."
No...But, if you're using pan (i.e. one characters voice panned 35 left and another's panned 35 right), you'll have a problem. Most mono recievers capture one channel (usually left), rather than creating a 50/50 sum.
By using the asymmetry function in the S1, you can shift the phase energy of one character toward the left and the other toward the right, without creating major level discrepancies in either channel. You can simulate the sound of hard left or right panning, while only causing about 3dB of level change. Therefore, listening in stereo, it sounds like the characters are panned to their own side. Listening in a mono sum will sound fine, as will single channel L or R...You won't have one character dropping by 15dB and getting lost in the mix.
You can also accomplish a similar effect by using delay. You can make one channel take priority over another, even though the levels are equal. This is fine for CD, but combined with the stereo widening used in on-air processing, it starts to sound really bad.