Not totally correct.
The voltage of that higher frequency is at the input terminal of the low section and vice verse at the high drivers.
AND, the slope of the crossover to each segment dictates how much current actually will be delivered to each driver. They are not brick filters, hence, you will get a pretty good amount of out of band currents in each section. It is that simple.
And ALSO like he had explained because the bass drivers would require more current than the other drivers the cable powering them would have a larger magnetic field around it which in theory could affect the high frequency cable due to induction.
Would he like to prove that this affects in any way the high frequency current? I'd like to see the numbers, thanks.
The same principle applies to not running your signal cables parallel to high voltage cables.
That 60Hz is somewhat a different issue, isn't it? that 60Hz is what would be coupled onto the signal cables, not other frequency. And, as far as speaker cables go, the high drivers slope would also control how much 60Hz would in fact be in the driver, period.
Perhaps before questioning and rolling your eyes at someone's quotes you should try to understand the science behind them.
Applies to you as well.