Note also that the Witch includes +2 cards, which means he's running with 6 card hands when he draws the Witches, which makes him more likely to have enough money to buy, first Gold, then Provinces. The extra draw also lets him shuffle faster, so he's seeing those Witches and money faster.
Edit: In other words, they're not BS hands, even though they feel like they are. I know exactly how it feels.