Come on folks, use a little logic and put down the paranoia.
This is not some Nigerian-type scam! You really think some crooked outfit just happened by coincidence to send checks to people who have had a specific credit card (many times years ago) and reference that card as why they are getting the checks?
Or perhaps someone hacked into American Express's computer systems just to get a list, then went to all the trouble to come up with a reason and official looking checks. However, if all they wanted to do was steal bank account numbers by sending fake checks, wouldn't it be easier to just send generic "rebate" checks to anyone in America? After all, how official and detailed are most rebate checks you get back in the mail?
Not saying there isn't some hidden motive (e.g. class action/government fine concerns) or Amex didn't keep good records, but let's refrain from the idea that the checks are a potential scam and weren't authorized by Amex.