That's probably a part of it, but the real answer is because an Amex is a charge card, not a credit card, which means that whatever is spent on it MUST be paid off in full at the next billing cycle. The net effect of this, is that if your customers are shopping with an Amex, they're people who /have/ money, or in the case of business cards they are acting on behalf of an organization that has money. Without writing an expository essay, it seems to be simply true that those who are more affluent also have networks and can bring people by word of mouth if you meet their expectations.
The primary reason Amex customers are more valuable is because most Amex cards carry an annual fee, which only more affluent folks can afford.
The traditional American Express card, though, is a charge card and not-withstanding the new Pay Over Time "feature", requires the entire balance to be paid in full every billing cycle. The entire reason they're popular with businesses is it provides an easy way to effectively do Net 30 payment terms without having to deal with POs and invoicing.
Why are Amex customers higher value? Is it because they're typically business cards rather than personal?