Could be both:
mechanical jam (as crew describes) preventing the throttle levers from moving into reverse detent (which is apparently required for automatic braking/spoiler operation) -
- and focusing on the TR jam distracted the crew (as they themselves note) from noticing that the spoilers were not up and the autobrakes did not go into operation, so they lost seconds before going to manual braking, and didn't note the spoiler condition at all.
Seems to boil down to the (still open, IMHO, from previous discussion) question of whether the plane could have been stopped had the crew immediately gone to manual braking and spoiler deployment (without TR) - on this slippery runway.