Too much bluffing and hoping in that scenario.

What I'm trying to understand is why AMEX sided with the hotel. Sure, hotel guests are responsible for room damage IF THEY PURPOSELY CAUSED IT OR IF IT WAS CAUSED BY RECKLESS BEHAVIOR. All you needed to tell AMEX is that the door was opened/closed in normal fashion and it gave out because it must have been ready to give out. I've had an AMEX card for most of my long life, and NOT ONCE have they not sided with me in these type of disputes. Plus they may have some sort of coverage for accidental damage.

I'd try working this with AMEX before getting involved with the CET bureaucracy. Depending on how long you've been a customer and what your charging habits are, you'll probably find them far more loyal than CET would be.