I don't think that either the OP or Amex is to blame here -- just very unfortunate circumstances. I have a hard time blaming Amex, as when you purchase something from a credit/charge card, you're effectively saying, "Amex, may I borrow $$$ for this purchase?". If someone came to me asking to borrow money, I would sure as heck say no if I wasn't sure that that person was who I thought they were, and if I thought that I was at risk of losing that money. FYI, there is a function on the Amex web site to pre-approve transactions on the Platinum charge card (a function that's needed because of the lack of a preset limit), but I'm not sure if it would have prevented this situation as it wasn't a refusal due to Amex not extending credit, but due to security.
If I were to blame anybody, I'd blame AC. You'd think they'd be able to make an exception given the circumstances and try to put the charge through again -- especially if those seats haven't been given away already to other bidders.