Correct. American Express has sent a reply, but not an explanation. American Express is a mass market company; they can send that reply to anyone. It reiterates the terms of the offer, but it does not explain which portion justifies your denial.
Don't be distracted by this. It's not important. American Express is not claiming that you had the card previously. They are merely making the point that there are several grounds for denial. Make them tell you the specific reason that your bonus was denied.
Thank you. Yes I will follow up as you advised - hope that leaving feedback to CFPB is sufficient since that's the only recourse left on CFPB.
In the past 24 months, only 1 closed AMEX card, and 1 AMEX bonus received (card still open), and I have a few long-standing AMEX accounts, so definitely surprised to see the pop-up.