IIRC the 1 handed thing is two fold, 1 it insures the non-firing hand is out of the way, 2 it promotes consistency of body position, and by relation consistency of shot placement. Although IIRC the practice of putting your weak hand in the same spot everytime comes from bullseye shooting, so I don't know how well it translates to defensive pistol.
The two handed thing IIRC is to put the final motion of the pistol perpendicular to the target vs parallel/tangent. If you drive the pistol forward any excess motion should in theory have less effect on accuracy than if you arc/swing the pistol up where over-travel or excess motion could have more effect on accuracy.
That's all based on cobbled together info, so I could be completely wrong, but that's my take on the explanations I've heard.