Only because there isn't an approach from the south to Sinop - you'd have to make a longer route to hit it from West Or East... While you can just head north in a straight-ish line via DETOS UW-99 ODIRA.
Departure practically due south. Of course ~ with relations being poor between Israel and Syria/Lebanon, there might routinely be a large detour over the Med, making SINOP slightly more probable... but I'd still favour DETOS/UW-99.
Another consideration indicating a turn at ODIRA is that the plot has the aircraft someway south of the nominal corridor ~ this could be the result of an early turn intended to make up time?
Some additioonal info:
1. Press release (google translation from russian):Plane, say local experts from turkish Flight Services Control, at 12:29 local time (13:29 MSK) on Thursday passed the airport flight information zone Samsun on the Black Sea coast, in 12.40 - left the flight zone of Turkey
Source 2. Press release from "Siberia" 1:OFFICIAL ANNOUNCEMENT of Siberia
Flight details SBI1812
The Tu-154 (RA-85693) was Flight SBI 1811/1812 from Novosibirsk, Sochi-Tel Aviv-Novosibirsk. On the way to Israel, landing in Sochi was performed in order to refuel.
The actual timetable (time UTC):
October 3, 2001
SBI - 1811 Novosibirsk - Sochi - Tel Aviv (DST 0909 - Vol 1338/1500 - TLV 1700).
October 4, 2001
SBI - 1812 Tel Aviv - point Rabit (TLV 0800 - RABIT 0944).
Estimated flight time based on actual weather:
Novosibirsk - Sochi = 4 hours 38 minutes, Sochi - Tel Aviv = 2 hours 08 minutes.
Tel Aviv - Novosibirsk = 6 hours 00 minutes.
The actual flight time:
Novosibirsk - Sochi = 4 hours 29 minutes.
Sochi - Tel Aviv = 2 hours 00 minutes.
Tel Aviv - RABIT = 1 hour 44 minutes.
Source 3. Press release from Siberia 2:
Official Statement airline "Siberia"
NOVOSIBIRSK, October 6, 2001 (12:00 local time).
Unfortunately, the media may be full of inaccuracies and distortions. Most often distorted by the following:
1 The Tu-154 (RA-85693) Campaign followed the flight number 1812 from Tel Aviv to Novosibirsk landing directly without intermediate in Bulgaria. Flight plan did not envisage such a landing.
2 Flight number 1812, adopted in accordance with the Russian civil aviation terminology, is a "charter on a regular basis." Departure of this flight from Novosibirsk is year round on Wednesdays. The first flight of "Siberia" in Novosibirsk - Tel Aviv was executed in 1995.
3 The exact title of Victor Alexeev, located in the crew of Flight number 1812 - The head of flight safety inspection airline "Siberia." It was not the deputy director general of airline "Siberia."
4 The exact title of Vladimir Tasun, head of the operational headquarters in Novosibirsk - the head of the West Siberian District Interregional Territorial Administration air transport ministry.
The airline "Siberia" will provide further information as it becomes available.
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Now, looking at map, that it could come up straight from ERGUN nav.point:

,
but "Siberia" also stated that the plane followed strictly the air roots (which is contrary to court documents....
Now should find out what is "airport
flight information zone Samsun"...