I find this discussion very helpful as well. Unfortunately, it is typical for AA to produce "receipts" like:

Fare Amount
Adult
1 × -$888.68 USD -$888.68 USD
AAdvantageŽ Benefits
PriorityAAccessSM $0.00 USD
Taxes & Carrier-Imposed Fees
Taxes $202.68 USD
Carrier-Imposed Fees $686.00 USD

The above is stated on the website. The actual e-Mails for purchasing and ticketing the ticket are both totally empty in the Receipt section. The above example is for a discounted J trip to Europe paid in cash and vouchers.

EDIT: I do think, however, that the receipts printed at the airport are often incorrect. I have one in front of me in which I paid a total of $2.9k for a ticket, suffered an INVOL re-route, and the "new" + only available receipt is only adding up to $2042.60.