The pads of your fingers are touching the keys, not the tips.Find E, F#, G#, A#, and B with your right hand. Position the fingers in the most comfortable manner. You should not be on your tips but the pads. This technique is great for control, much better than the classical technique because you have less contact with the keys with just the tips.
Horowitz I believe was one of the original flat finger players, and I must say, don't even try to copy it. Horowitz had a very different technique. Just watch him. Flat fingers, low wrists, curled pinkies. All things we try to avoid. However, Horowitz is Horowitz. Definitely not something that could be copied.