This has not been my experience. As I mentioned above, I had this exact problem with American Express a few years ago. At that time their systems always accepted foreign charges, they could not stop them without changing their software. The charges even followed me through all the fraud alerts we posted and even when I cancelled the card and got a new card issued.
I assume that they had strong business reasons for always allowing charges to be posted and leaving it was up to the cardholder to decline the charge. Ultimately they solved my problem but I assume these business reasons probably still exist so I no longer trust any cc company to protect me from fraudulent charges.