I just thought of something. What if the ship going down isnt the enterprise and is the ship that spock was reassighned to. It would make sense beacuse the part where it is crashing into the bay it doesnt look like the enterprise. Also There was a interview on trek web where the producer of into darkness says are you sure its the enterprise falling through the atmosphere. Also spock is the captian of the ship during the falling sequence and orders an evacuation as the ship falls. Also its possible because kirk was demoted to first officer and spock is in cammand kirk could be spocks first officer.