I agree that was a little unclear. I think what he's saying is that since humans can't hear above ~20 KHz, frequencies above that are lost. The 'wobbles' in the square wave are what happens when you take a square wave (which is a summation of infinite sine saves with frequencies an integer multiple of the fundamental) and drop the frequencies above the ~20 KHz cutoff.
In other words, it has nothing to do with any analog/digital conversion. It's just what happens if you ignore frequencies above 20 KHz, which we can't hear anyways. We can't hear any difference between a 'perfect' square wave and the bandwidth limited one.
I also don't completely understand about their being only one possible solution. It makes sense if you know that the signal is a single sine wave, but since in general the signal is a summation of an unknown number of sine waves, it's not clear. I guess this is something he didn't have time to get into more depth for the quick overview :)
> Isn't there also an argument that frequencies above 19khz
The rule of thumb I've heard is 20 KHz. I also wondered if this is an issue. It'd be interesting to know the distribution of how many people can perceive frequencies how much higher than that. I think though that the 20 KHz is already fairly far along the long tail, and most people's cutoffs are actually lower.