For the impact that occurred here, it is not surprising that the horizontal stab was identified in the wreckage. It will have less fragmentation than the forward parts of the aircraft. The wings would have substantial fragmentation, but inner span sections of the spar will be identifiable, The engine cores (shafts, gears, not necessarily aux cases) actuators, control, gear, flap drives etc, would be usually in identifiable components, the further back in the structure the less fragmentation of associated quadrants/cranks etc.
The presence of the stabilizer doesn't rule out some control issues, but it still remains a remote possibility for initiating events. Had parts of the stab been found 12km away it would be a point of interest, but absent that it is not indicative of cause. Even if found 12km away, the failure mode would be of significance, as would be the trajectory analysis of the part to determine when it would have separated. Controls are not indicating a factor as yet other than the obvious fact that the plane didn't get to its destination, so presumably, at some point, the flight path was not as desired, or not.