Just thought I'd add one more Amex story that was really kind of amusing.
When we applied for the Optima, a letter came back saying we were declined because my husband's facility has an unlisted phone number.
We called back and explained that he works for the Federal Aviation Admin (the what? - ummm, it's part of the US government) in a facility that has no contact with the public, so no directory assistance listing. We offered personnel's number, pay stubs, etc., but was told no phone listing, no card because apparently they didn't believe this place really exists and, I guess, we could fake all that other stuff.
Told them we used to have gold cards and he had the same employer at that time. No dice.
Then we said, well let's see, his FAA expense account credit card is an Amex. So someone there knows the FAA exists and believes my husband works for them or they wouldn't have issued the card. "Ummm, let me get back to you," the sup said. Two weeks later the cards arrived.
I've never before or since heard of a listed phone employer number as a requirement for credit.