I would call AAdvantage back and speak with another agent. If they also say no, then ask if you can double check with a supervisor. Unless something has changed in the last few months, AA should be able to do this.

I did this a few months ago--added an infant lap ticket to a reservation booked using AA miles on an Iberia (transatlantic) flight. At the time, I also had called Iberia to see if they could add the infant to the reservation, and Iberia said no, since it had been booked through AAdvantage.

(As an aside, you can see the cost of the infant lap fare on matrix.itasoftware.com. If the adult ticket is a transatlantic round trip fare in coach, the infant fare is usually around $100, give or take. Business class or one-way tickets are much more).