When I applied for the AS Visa card in August 2008, it was my first (and so far only) credit card. I was approved for the Platinum Plus card, not the Signature. The Platinum Plus has a lower sign up bonus, I think it's 5K. If your wife has never had a credit card of her own before, I'd expect something similar.

I've had my card for almost three years, have paid on time & in full every month (even paid early a couple of times), and have a credit score of 781. I'm hopeful that when I next apply for a credit card, I'll get the full/premium version of whatever I apply for.