This is a lousy situation, as there's no recording of what was said. AA corporate can't verify the facts (even if they wanted to), so they can't pin down which version of the facts is correct.

Passengers lie all the time -- that fact is well known and we see it every day. I still remember when airlines allowed non-refundable fares to be changed with a doctor's note -- a deluge of sicknesses ensued. I am sure that if asked, the employee's version of the facts is that you're simply lying and are trying to bilk the airline some money not due to you.

It's still worth sending a letter: it will go in the employee's file (the voucher will trace back to him/her) and he/she may be "retrained" if enough of those pile up.

Moral of the story: airlines are protected from lying employees (believe it or not, this is written in the airline's contract with you, and it's legally allowed by Washington!) so they don't do much about it, and therefore you should always have everything in writing and reread what doesn't seem to make sense (bag fees? really?). And take an airline's reputation in consideration, not just the ticket price, when making purchases.