Maybe that's more than one question....
Based on several statements and other information publicly available at the time of the interview controversy, and despite holding only SLF/attorney status here, I'll take a swing at part of this. The primary basis articulated by the labor union representing the AA aviators was that recording of interviews imposes an unwarranted and unnecessary atmosphere of formality and even an adversarial posture, whereas the interview is supposed to be more aligned with purely investigatory factual inquiry and reflective of a "just culture" approach., (This is only my description of the APA's position and I'm not quoting anything or anyone.)
My understanding is that there was an airline labor-management issue that was part of the context, or background or backstory - or at the very least, the issue very likely could have been part of the context. IIRC, the APA had objected to some changes in flight deck procedures being implemented - perhaps "imposed" would be the correct word - by management without participation by and/or consultation with APA that the union understood to be required by the collectively bargained labor agreement. The issue concerned how the airline management requires the PM to deal with checklist items in the time period immediately prior to departure, including taxiing to position for takeoff. I apologize for imprecise terminology if I've used any here - although I'm pretty certain APA had stated concern over a change management had imposed about the specific workload and task items to be completed by the PM during that time period.
The change had been imposed just a short time before the incident The linkage is that some reporting at the time indicated that the PM of the incident flight had been focused on getting these new procedures done correctly, to the detriment of what otherwise would have been more complete and/or intense focus on clearances for taxi and takeoff. (I realize the thread has included comments on the tasks to be completed by the PF, and it could be that APA's actual interactions with management had included discussion of how the new procedures would affect not just the F/O (in this case) but the PIC as well.)
If this much is correct, then in addition to a general sense that the incident was ripe for finding a bus, grabbing a couple of pilots, and tossing them under said bus, the union also was concerned with not compromising its issue over the implementation of the new procedures - and also guarding against its position being co-opted by the inevitable attention-payers swarming in - competent press and media; the rest of the press and media; the Congress, et cetera. (My observation of a "general sense" of blame looming over this incident relates back, and it relates all the way back, to the way the Executive Branch has run the Department of Transportation and the FAA, but let's not get political or anything.)
As to how and why the crew continued on to LHR and the rest, I can't say anything useful.