I mean, neither citi nor chase ask for SSN of the additional user (they only need a name). Why would American Express want SSN? Does AmEx run credit check on the additional user?

AmEx really makes things difficult for card holders. In addition to asking for SSN of additional user, they also make you wait for a month before you can use your points from last month's statement.

No way I am keeping AmEx after I squeeze out all the benefits.