Not true.

I was talking to Citi about a separate issue. The rep asked if I'd like to apply for AA card and get 25k miles. I told her I already had it, and she said I should get another one anyway. I stated I didn't think it was allowed, and she told me the last person she spoke with already had 4 cards.

Having said that, Citi does limit you to 2 applications within 60 days. But that is for all accounts, not just AA MC.