US CC issuers do allow partial disputes and for exactly the reasons set forth here. It is little wonder that AA did not contest the dispute as, by its own COC, OP is due a refund of at least what he disputed. Whether he pursued as a refund or a dispute is of no consequence to AA.

So why didn't BA reroute OP? Most likely too much of a hassle for a handling agent at an outstation. One carrier handling for the operating carrier flying a passenger on a third carrier's ticket. Crazy in 2016, but that it is.

BA will likely properly assert that it is not liable for EC 261/2004 IDB compensation (or for the ensuing delay/cancellation compensation) because no valid ticket with a reservation existed. AA won't pay up because it was not the operating carrier and EC 261/2004 does not apply to it. Additionally, it will already have told DOT that it would have issued a refund had OP asked, but OP sought a chargeback and AA did not challenge that.

OP has roughly EUR 1,800 per person on the line here, so no small sum. But, at lease he is not out any money.