I've been looking at different cards on Amex's site and noticed that BCE has a Welcome offer: Earn a $100 cash back with $1,000 in eligible purchases in the first 3 months of Card membership on your Blue Cash EverydaySM Card.
The fine print: Offer valid for first-time American Express Cardmembers only. To qualify for the $100 bonus, you must make purchases with your Blue Cash EverydaySM Card from American Express that total $1000 or more within your first 3 months of Cardmembership. The bonus will be awarded in the form of Reward Dollars, which will be added to your Reward Dollar balance 6-8 weeks after the spend threshold is met and can be redeemed at any time at a minimum of 25. Cash advances, balance transfers, interest charges, fees, and the purchase of American Express® Travelers Cheques and American Express Gift Cheques, or other cash equivalents, do not apply. Additional Cardmembers on your account are not eligible for this offer. To receive the $100 bonus, account must be active, in good standing, and not in default at the time the statement credit is posted to your account.
So, what I'm wondering is if I haven't had an Amex since the 80s, would I qualify (if approved, of course) for the rebate? Has anyone gotten their welcome offer with an ancient, closed Amex? If you're no longer in their system, would that make you a "first-time" cardmember?
Of course, I realize this is a more difficult card to be approved for, but it's the other one I want besides Costco. 
Thanks! 
Okay, thanks. My last amex was from the 80s.
Glad you brought this up,
I had apped for the Blue Cash 3/11 approved, I apped for the PR Gold 7/11 approved and I apped for the Blue Cash Preferred 10/11 approved, and there was an offer for 100 cash back if I spent either 750 or 1000 in the first two or three months (but was only good for New AmEx applicants) I did my app for the BCP over the phone and I asked the lady who took my app if I was eligible for this promo even tho I was an existing AmEx Blue cardholder, she put me on hold, and when she came back, she said she had spoke to her manager and he told her yes to go ahead and apply that promo to my account.
Long story short, I spent the required amount the very first month and PIF before the statement cut, I had totally forgot about the promo and when I did check my cash back about 2 weeks later I had 107.71 (or so) cash back. (last I checked I had just over 137 in cash back, not including this cycle, I've run just about 1K thru it this month, 85% of that at the grocery store 6% back and the other 15% for gas 3% back) Love taking $$ from CCC's
So as another replier has said, AmEx can make exceptions, it's just up to them weather they will or not.