Phase cancellation is a common cause of confusion for many audio professionals, sometimes this is caused by a channel becoming inverted for some reason. Maybe this answer can help you, and other people reading this, to identify, or eliminate this type of phase cancellation as the cause of a problem.
I've analysed the audio from the video and have come to a conclusion:
Mike Mangas(First Guy): Second Channel is INVERTED
Jennifer Scarborough(First Lady): Second Channel is INVERTED
Kelli Saam(Second Lady): Second Channel is INVERTED
Allison Woods(Third Lady): Second Channel is INVERTED
Evan Schreiber(Second Guy): Second Channel is NOT INVERTED
Music : Second Channel is NOT INVERTED
Analysis: Looking at the stereo waveform snippets, we can see that for some of them, the second channel is inverted(upside-down). So the value of any given sample on the first channel is being cancelled(ideally) by it's opposite(negative) value from the second channel. So when the two channels of the stereo signal are summed together, i.e. when played as a single(mono) signal, phase cancellation occurs, resulting in little to no signal.
Conclusion: The only audio that does not have an inverted second channel is Evan Schreiber(Second Guy) and the music. This should help you figure out what caused the inversion on the second channel. i.e. Whatever processing you did to the Evan Schreiber(Second Guy) audio to copy it to the second channel, worked the way you wanted. What ever you did to the audio from the other presenters, caused the problem.
How to Fix*: I have looked into the 'Fill Left'/'Fill Right' effect that you say you used, and it shouldn't invert the copied waveform. If you still have all the separate audio feeds on different tracks in a Premiere project, simply repeat the 'Fill' effect to copy the first channel to the second channel. The inverted waveform will be overwritten. Another way to do it is in Audition; Open each of the problem files, select the whole file and deselect the first channel. Then go to the effects menu and select 'Invert' this will invert the second channel, solving the problem.
*NOTE: To apply the fix correctly, you have to apply it to the dry audio, where no stereo effects have been applied.
P.S. You can actually hear the effect of opposite phases in the left and right channel with headphones on. Listen, and in the future, you should know how it sounds. It sound's like the left and right channels are 'fully separated', it feels kind of awkward. Try switching between the Evan Schreiber(Second Guy) audio, and one of the problem ones, and you should notice it.