The flight is indeed a parabola – as are all jumps. Once the center of mass (COM) is in flight – the path is unalterable. Yes, the body segments can be moved relative to the COM – but the COM flight is a constant parabola.
The misconception seems to come from the fact that the take off distance before the hurdle is approximately twice the landing distance from the hurdle. But keep in mind that the COM is not into flight until toe off of the plant/take off leg. If you consider the classic hurdle takeoff – with the athlete leaning well into the hurdle – the COM is well beyond the takeoff foot and much closer to the hurdle. So the actual flight of the COM is much shorter than the take off to touchdown distances.
Not sure if it’s folklore or just because its been repeated so much (that the hurdler is coming down over the hurdle) – but most studies show that the actual peak of the COM is just in front of the hurdle. While not actually over the top of the hurdle – its only a few inches/cm before it – with the difference negligible.
McGill’s description of his proposed technique implies that the flight has a rapid vertical rise and a gradual descent…which isn’t supported by physics. I won’t get into the horizontal velocity loss required to rapidly raise the hurdler vertically.