The more I have read about this incident the more egregious the mistakes on behalf of the AA crew appear to be.
(1) Not knowing which runway you are supposed to taxi to
(2) Missing the turn for the correct runway
(3) Barreling across an active runway - apparently without checking that it was clear

To make matters worse, they then proceeded on the flight, in the process erasing the CVR data from the incident.

I know that I certainly would not have felt comfortable continuing to London with that crew.