From my personal experience... once a restaurant charged me twice (exact same amount on the same date). Dispute the charge and no question asked.
In the last 2 months, I have ~5000$ charge to my card from some resort in Nassau. I told AE that I never been there and I was in Tahiti during the room charge occur (with prove of travel document). AE said they will do the investagation and in the mean time I was given the credit for the amount of disput.
I will never pay the 5000+$ even if they couldn't find out who really make the charge or if I have to get a lawyer to defend me on those charges.
Still waiting to hear from them if they find out what happen.
Cindy