@Spike, indeed, Zanz doesn't directly say that, but he talked about 14 cards. Unless he was simplifying the situation, he must have been talking about the Mulligan which draws a new hand from the now 23-cards deck.
@Dictator, yeah, I think I will, sooner or later. Running some math, if in 6 games where a mulligan happened and there were no zero-cost cards even after the Mulligan no zero-cost cards appear in the next 7 draws, the probability of that being a coincidence is under 1%, so it must be true. I will try it.