The turning issue is a bit of a red herring TBH, as observed, the Captain will decide according to his/her wishes. I am curious to understand how a 737NG can still have TOGA auto throttle more than 2 secs after ground air switch senses touchdown or with a TRA split of more than 10 degrees? This theory would mean they landed with the A/T armed and then somehow pressed TOGA before 2 secs and then selected asymmetric reverse? seems like far too may swiss cheese holes! Regarding info from "someone on the ground" having been based in Trabzon for 6 months I would take that with a very large pinch of salt..
Of course being Turkey its possible the Captain lit a cigarette and dropped it, lent forward to catch it and opened the T/L, after the Correndon fire at AYT due smoking we wouldn't be surprised!
Dongle..Can you provide refs for the uncommanded asymmetric TL movements please