My guess is that TWA/AA get paid 2 cents per mile from AMEX and this would actually be a cash benefit.
These guys all have major incentive program initiatives where they sell miles all day long at cpm.
My understanding is that the only reason AA is not in the AMEX program is that they agrreed to an exclusive with Citibank on the Avnatage credit card (Citibank owns Diners, hence their participation there), but it's not as if they don't want to sell miles.