Look at how close that plane is to the Russian border when shot down.
How do you mistake a plane as military and threatening that has flown 80% of the way across your territory at a fixed 33,000 feet on a fixed path that will be out of your territory in a matter of minutes.
Exactly the same way that the USS Vincennes shot down the Iranian airliner in 1988. You are profoundly ignorant of how flight control communications works. All the controllers scattered over thousands of square miles of airspace are not tracking every flight. What you describe is an impossible oversimplification, which is reason enough to wince.
In retrospect, everything you say makes sense. In real life, at any given moment in any heavily trafficked area, not so simple.
The complicating factor seems to be that whoever fired the missiles was even more ignorant of the different frequencies possible to attempt to communicate with a specific aircraft in the area, (a reasonable expectation before shooting down a suspect aircraft) whether the transponder data was even checked (military or civilian?) before making the decision to fire.
I won't even attempt to understand the complexity of the additional time and multiple steps necessary to prepare the missile system to fire, while, presumably, the suspect plane is verified as hostile and threatening. Every aircraft within a hundred miles? I don't think so.