I'm sorry that happened to you. If I were in your shoes, I'd probably never do business with Amex again. But your problem was you didn't have 12 Amex cards, you had 1. Amex sells a lot of flavors of cards, but at the end of the day, they're all tied together. You're dealing with one lender.
But the topic is: Do they have the right to do an F/R? They do.
Do they do a lousy job of implementing it? No question.