What kind of AmEx card? And what terms on your hotel reservation. Did the hotel really charge you a deposit or was it a prepaid reservation? Most hotels will do a credit card authorization at check in to cover any additional charges (such as room service, phone tolls, etc.) and/or damages.

BTW, I've stayed in a couple hotels overseas that did check the room before finishing my checkout. I noticed this in particular at one hotel in Istanbul and also a local hotel in a smaller city in mainland China. It might have been done in Greece too.