Why are you that sure that the plane was in Syrian sky?
Turkey knew fully well it was a bomber from its signature and velocity. They could easely intercept in above their own ground and make visual contact. They could have very easely seen that it was a russian plane by the huge red star on the tailwings.
The missles on that F-16 got a range of nearly 20km. If Russia's story is accurate and the closest it got to the border was still 2-3km in syrian airspace, then it would have been very easy to take it down while staying in their own airzone.
Erdogan also said that "there are no rebels at the border, so bombing the border is bombing turkmen".
