I certainly can see your concern, but if I were in your situation, I wouldn't be too worried. Even though the false E-mail is valid, it may well not be in use or frequent use. Even if it is used, the other user may consider the E-mail to be SPAM, phishing or whatever. Even if none of that is true and a real user opens and gets your E-mail, I think it is unlikely that the person would have any desire to get in and fool with your reservation. I certainly would not.

In your shoes, I would have AA put a note in my PNR, I would check up on my reservation periodically, and not worry beyond that. If you're really restless about it, you could always try to E-mail the other person with the similar name, but I probably wouldn't.

How long until your first flight on that PNR?