Yes, that's right. I misremembered.

I like your argument that all the balls in the urn are labeled good/bad and drawn/not, and that two processes are causally orthogonal, but it's not so simple as each ball being independently randomly labeled. It's more like: sample without replacement some number of balls and mark them Good. Then replace them all, and sample without replacement some number of balls and mark them Drawn. Naturally, I mean for a full random shuffle of the balls in the urn to occur before both samples are taken. And, as you observed, we're asking about the distribution over the number of balls with the labels (Good,Drawn). Looking at it that way, I'm absolutely convinced. Thanks.