That's interesting. I've never had my bp state Sky Club as an Amex Platinum holder. I have never bought a pass, but isn't it possible to buy one directly from a SC agent?
http://www.delta.com/content/www/en_...-day-pass.html
If so, what I would do is go to the club and if you get access based on your bp, then great. At least you may get in for free. If not then just buy the day passes on the spot.
To get into a Sky Club as an amex platinum holder, they need to swipe the card.