Quickly skimming the post, I think the key is that the OP had several tabs open in the browser. My experience is that this can cause problems with sites where you are logged in in a secure way (
https://...). You might believe you are working in one tab, but strange things can happen like that described because the site is still really securely open in the original tab only. Just a thought...and I don't think it is an issue particular to AA.com.