I realize this may just have been a negotiating ploy, but you may not receive a different answer from American Express. Their charge cards have no preset spending limit, but that is entirely different than having no limit.
Yes, negotiating ploy. I did call AmEx and ask "What happens when I swipe for $250k?" The individual on the other end said, "We might call you to verify it if you don't have a history of such transactions, but it will be approved." I'm still not sure I believe them, haha.