I can see where he's coming from. Intuitively it seems wrong...but after looking at the graph it seems to me that it could be true. Every time one wave peaks, the other two waves each have a magnitude that is half as large, and half the magnitude. So for every peak, the other two waves have a sum that is the same magnitude as the peaking wave, except it's opposite polarity so they would cancel. And every time a wave crosses zero, the other two waves have polarities that are of equal magnitude and opposite polarities so the sum of all three would be zero.
EDIT: I graphed it out in MATLAB and it appears that
0 ≡ Asin(ωt) + Asin(ωt-2/3*pi) + Asin (ωt - 4/3*pi)
so the cancellation seems to hold true for all areas of the curve, not just the peaks and zero crossings. But 0V at a single node does not mean no current flow. After all, a common short is some +V connected to 0V.