From what i read about it, there is no consensus yet on this one. On the video you can see that he turns his head completely around just before the shot, then turns back again just after the shot.

The truth is that Greer acted badly once the shots rang out.

Instead of accelerating, as he was trained to do, Greer actually slowed the car down to a near stop, before he was forced to accelerate by Clint Hill who screamed at him to get to a hospital.

Greer subsequently said that he did accelerate but the famous Zapruder home movie proves the case against, him as well as numerous eyewitnesses.

( source: https://www.irishcentral.com/roots/history/did-irish-william-greer-cause-jfks-death )

So he also lied about it.