I still remember one of my professors telling me once, when we were looking for a particularly sharp sound on a note in a piece (I think it was somewhere in Copland's "Variations for Piano"), holding his thumb and third finger together and banging down on the key from about eight inches. "That's your 'weapon'!" he grinned.
You would be well served by looking carefully at some of the videos of great pianists. You'll notice that there's a good deal of variety in their approach to finger technique, indeed, whole schools of study are built around different approaches to it. The Russians tend to like to hold the fingers up some from the keys and sort of plop the down flat-fingered (look at Shura Cherkassky for a representative example); Americans (who haven't studied with Russians, perhaps) tend to have a more curved hand position. You'll notice that Horowitz appears to do this, but careful inspection will show that while he often holds his fingers out flat, he pulls them in when hitting notes in a sort of plucking motion. You also might notice that his very rapid finger passage work is rather non legato; the notes get his trademark clarity by slightly disconnecting them one from the next. I think that plucking motion rather assists in getting that sound. You'll also notice that he is very still from the shoulders down, getting a lot of his volume from very rapid and percussive arm movements.
If you compare Rubinstein, you'll notice that there's a lot more moving around of the arms, but the arm technique is less percussive than Horowitz's. He gets a softer sound with bigger movements. You'll also notice that his finger passage work has less up-and-down movement of the fingers; the fingers start closer to the keys. Look especially at, say, a quick run of notes in a Chopin piece.
A lot of how far you raise your fingers when hitting a note has to do with the level of volume that you want. You can get a lot of volume without raising the fingers at all, by putting body weight into it, it is true, but you can't play very fast that way. And, you can also do it by raising the fingers higher and still get a great deal of speed.
So, the short answer to your question is that you have all kinds of tools in the box, and each has its place.