I got a dead link the first few times I clicked on the link. I thought I might call the phone number in the OP, but I had second thoughts about calling a phone number and divulging my credit card number (and confirmation code) with no other verification of authenticity than an internet forum posting (nothing personal, LastSurvivor). But after a few more tries, I got the link to work, and the address it takes you to is the www109.americanexpress.com domain that we've seen before in legitimate postings, and the page at that address lists the same phone number as in the OP. So if you can't get the link to work, my interpretation is that the phone number is legitimate.

I also was ineligible.