The JFK RELOADED "game" made this clear. When he makes the turn, the target is moving more than when he is slowly heading away. If the game were still active, i would post the shots. I tried it both ways (basically, in the game, you are Oswald), and it was way easier when they were heading away from TSBD.
Before the car turned on to Elm -- the windshield -- bullet resistant glass -- and other 'targets' in the way.
If he had done it when the car was directly below, (fishbowl) he would have had to lean out the window making him a visible target and in a very awkward position.
From his little snipers nest built of boxes of books he had a perfect stand to rest his weapon on and make totally unobstructed shots after the car past.
Go stand in that window some time and you will realize how damn easy those shots were.