Flying to Mexico - MIA-CUN-MIA .. Ticket booked on AA's UK site for 2 adults .. Called up AA reservations this morning to add the infant to the booking

After a rather lengthy call the agent told me it was done and there's no additional fare nor any requirement for an e-ticket to be issued for the infant because "it is a domestic flight" and I just need to checkin at the airport and the infant will get a boarding card

Now obviously it's not domestic - but maybe US - Mexico has the same rules for lap infants as domestic ?

Can anyone advise if this is correct ... I also have an AA international ticket (Europe - South America which this is an extra side trip) and for that I called up reservations and they charged 10% of the adult fare + a few taxes which I thought was normal and the infant got an eticket issued etc. ... I expected the same process for the MIA-CUN flight ... obviously if it's free it's better, but it seems a bit odd .. I challenged the agent a few times but they were insistent that this was the case for MIA-CUN

Thanks !