For what it's worth, nothing in the PAPER offer itself says anything about not having had this card before to be eligible for the benefits. The offer on paper is ironclad. And as I noted, TSMRSRNE has already begun to receive bonus miles, despite having been a cardholder before.
I will hold onto the paper offer as well- as u mention OP there is nothing there about previous card member- in fact they add the bonus miles to her current balance in the lower left hand corner of the paper offer to show how many miles will end up in the account!