IMHO, Amex did not (at least correctly) tell you the charge could not be disputed as this is your absolute right under the Fair Credit Billing Act. But, get on it fast. You must send a written dispute to Amex within sixty days of billing date at special billing error address on your bill. DO NOT rely on a phone call.

I have done lots of these and have never had a problem once the legally required WRITTEN notice is made.

Good luck.