I applied for my Amex Zync on 12/30/2011. I was able to use the card to purchase something that day, because they immediately give you your card # online after approval.
When the card came, it said "member since 2012". My online account said the same thing. I called Amex and they changed it to 2011. Now when I log on to the Amex site, it says "member since 2011".
Thanks JustMe. I had recalled that some people had that experience but couldn't for the life of me remember the exact details. Thank you for sharing your experience.