I don't think Daichovo means that the denial is unusual, but rather the delay in proving the formal explanation for the decision.
From American Express's perspective a charge card represents lower risk than a credit card. Don't be mislead by the way that No Preset Spending Limit is marketed. This feature allows the lender to keep its exposure very low, and it can declare the account in default if the entire balance is not paid each cycle. With a credit card they can only declare default if the cardholder fails to make the required minimum payment, which is tiny.
I am quite aware of the ** No Preset Spending Limit. But on a gross income of $18k per year, you would likely only get a $1k-$2k credit limit on a regular revolving credit card. On a ** No preset limit card, they would most likely put the exposure at somewhere between $500 and $2000. Though, I agree, you don't have the option of a small ($25) minimum monthly payment. But, still, from AMEX's perspective it doesn't sound like a "right fit" vis-a-vis card product and customer (income).