There is a region in Spain that has a long tradition of the young ladies practicing with their knives on the local cork trees, in a very effective manner, with the point down for much of their "attack." Primary targets when standing being both sides of the neck and both eyes. I'd rather not get into primary targeting if already taken to the ground. Of course this is intended as defensive work.
But from the outset, much of the stuff one sees on back and forth "duel style" blade fighting is b.s. Knife work tends to be down, dirty, and fast, often over before the loser knows it began.
In essence, the blade can be well employed held either way,,,, as circumstances dictate. Stand half an arms length from a tree, imagine your target area, which grip is easier to stab or slash at the gut, which grip is easier to stab at the eyes or neck, what about down through or behind the collar bone, which grip to slash at the neck or throat? Now stand closer, and further, how does this change the preferred grip for a given target? What if the adversary is taller than you? Shorter than you?
Which targets make an adversary not want to play anymore the quickest, what about minimizing your contact with their blood, viscera, and other bodily "fluids"? (It would suck to win that fight only to end up with h.i.v., hepatitis, or worse, if it can be avoided)
These movie fights are choreographed just like the dance moves in music videos and movies/stage productions like "West Side Story." Some are done better than others, but it's still too slow, and too clean.
