I'd edge towards saying she is right. While other techniques can differ, having your palms parallel to the floor can be dangerous. It's quite common for a hook to be lightly off when you hit. With your hand like that, if you fall short of the target you could catch with just your two end knuckles, which I know from experience can be a nasty injury. With your hand the other way, all knuckles will hit at the same time, regardless of wether or not you fall short, so it distributes the impact much better.
A. Overeem : G. Nelson : R. Khabilov : T. Means : C. Mills
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