I think thatīs there is a big difference between "the correct way" to hold a knife and "the best way".
I don't know about anyone else, but I hold the blade down or inward. Think about the mechanics of how your hand works and what else you are concerned with in a hand to hand fight with a knife. The way your arm and hand ,works, cutting across your body...well it makes the most sense IMO to have the blade facing the way you can use it. Cutting back across, you rotate your hand over to cut in that direction.
It makes no sense that I can think of to have the blade facing up on a single edged weapon, it limits the use of that weapon IMO.