I've had something like 15 inquiries on Experian in the last twelve months and was approved. And I'm probably in a more precarious financial position than most people (I'm not going to delve into my personal life here).

Legitimately, this is the first time I've heard of anyone being denied for this Amex offer that didn't have a returned payment (there were two people I read about who were denied for that reason). I'm sincerely surprised since it seemed like Amex was just letting almost everyone get the card.