You're wrong.

I don't know about appying for two identical cards at the same time, but certianly you can apply for another AA MC when you already have an AA MC open.

The problem is not at Citi, the potential problem is just you yourself getting confused. I tend to look at the card casually when I pull it out of my wallet, not examine the card number carefully. So I prefer to have only of each look in my wallet. Thus I would rather not have two of the same type that I still need to carry around at the same time (say, an MC I'm keeping long-term plus a second MC I just got for the bonus).

My presonal strategy is to keep the Visa longer-term (both because it's got the lower bonus, and because it's the only way I can earn AA miles with a Visa and sometimes certain hotels have bonuses only when paying with Visa), and churn the MC and Amex back and forth more frequently. That way I only need to keep the Visa and either MC or Amex (but not both) in my wallet, and there's not much confusion. I plan to only churn the Visa about once a year, around annual fee time. )