There's a fade up at the start, and typically at 4'20" where the volume drops to zero. That black line is the zero point in the waveform, and if there was a DC offset that's where it would show - not on the peaks. The DC offset adjustment was dropped years ago, because the issue that introduced it has been eliminated with all modern sound devices. The phase shifting technique is the usual way to reduce the assymetry. The cause of it is simply that positive peaks in the waveform are larger from some sources than others - typically brass instruments are prime suspects, but the human voice can also do this. It's always positive because it's a breath offset, and forward breath is by convention always shown as a positive excursion (it's nearly impossible to make a significant noise whilst breathing in). Incidentally, on your original screen-grab, the lower channel appears to be polarity-reversed; the assymetry is going in the wrong direction.
Anyway, if you had a DC offset control available, adjusting it with those waveforms would actually introduce an offset!
There are other ways of 'correcting' this percieved problem - typically if you have a lot of short peaks, you can use a limiter to reduce them, and with care you won't notice the difference. But, it only really matters anyway if you are trying to extract the maximum loudness from a track, as those peaks limit the maximum excursion.
Personally I'd get the channel phase sorted out and leave it alone, but of course it's entirely up to you what you do. But no, it's not a DC offset.
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