I did Google the number but it didn't come up with anything more specific than "Manhattan".

Just called AmEx via the number on the back of my card--this was a scam. The 212 number is not associated with AmEx. Interestingly, overnight I also got an official-looking e-mail with the same info saying I'd been invited and asking me to call the same number. This is not your typical amateur scam--both the phone call and the e-mail could easily be real. No obvious typos, crazy redirected e-mail address, or other dead giveaways. Also interesting that the scammers got my cell phone number and e-mail address, and know that I have an AmEx product and am interested in Centurion.

So fellow FlyerTalkers, beware.