While it would be close to LITERALLY impossible to rig the draw (off the top of my head I can't think how it could be done or, really, who would want to do it who would actually be able to) I do agree it is unbelievably lucky for D/W that they got the final spot in both programs. Odds of it, while not astronomically low, are low enough that they should be thanking their lucky stars.
Maybe that's why Meryl is wearing those sleeves. They're stuffed with #20s! (In actuality, I have no idea how the draw works. I'm assuming numbers in a bag?)