The important part of the lead is the guy initially pulling downward and towards his right hip before then raising his right arm for the lady to turn under. The hand grip is not important.
What I would say though is, when it is usually taught, most teachers use the analogy of bowling a cricket ball. When the guys do this, their hand naturally twists to have their palm facing upward (rather than the 'usual' palm towards the guys, back of their fingers towards the ladies) which has the effect of changing the grip to your 'fingertip hook' grip.
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