While I am not big on credit card disputes (never done one for a hotel reservation myself), this might be an instance where you do indeed want to dispute it with AMEX.

--Jon

P.S. I also don't make non-refundable advance reservations. The typically small savings isn't worth it to me. On the other hand, if your travel arrangements are typically very firm, than using non-refundable advance reservations may be worth it. The occasional forfeited reservation would just be a cost of using them. Depends on which will save you more money in the long run. Each to their own.