It actually depends on who you ask. The map in post #2 (thanks, McGruff) shows that the incident happened over Turkey's Hatay Province. Hatay Province was annexed by Turkey in 1939. Before that the province was aligned with Syria.
The Syrians have never recognized the Turkish annexation of the region. Below is taken from the Wikipedia article on the province:
Syrians hold the view that this land was illegally ceded to Turkey by France, the mandatory occupying power of Syria in the late 1930s. Syria still considers it an integral part of its own territory...Official Syrian maps still show Hatay as part of Syria.
I read today that the reason for the shootdown had to do with a video. But what difference does it make?
That was my point - it’s unclear. The area is disputed, and even NATO is shocked that the Turks didn’t simply escort the plane out. What Turkey did was reckless and uncivilized, but that is how the crypto-Islamic Turkish government rolls.