It's a double edge sword. You don't want it to be too easy to get an email address out of an account because then someone could fake being you and suddenly you don't get any of your emails.
It hasn't happened to me with AA, but I have gotten dozens of incorrect emails. My favorite was a pizza company in the Netherlands. Someone had put my email address for their account and every 1-2 months for 2 years I got a receipt for a pizza delivery. The person calls in the order, says so in the receipt so I have their telephone number and physical address if I ever want to make contact or a long distance call.
If I've tried everything and want it to stop and can't, I go to the account, request a new password sent to the email address of record, which is mine, and change the information myself. I did this for someone with a Walmart retirement account. I didn't want getting their retirement information emailed to me every month.