I've often wondered if this was the case (each person is born with a certain amount of technical ability). No, I don't believe this is true. Piano technique is lots of things, not just musical means, but also agility and reflexes. If you have talent for the instrument, you can be taught how to develop your piano-playing muscles in your hands, hand flexibility and pianistic instincts. All this is not only taught and learnt, but also developed. You need to do proper training in order to develop the hand coordination (strength in arm and hand) that allows you to play faster without tensing up. I like to do a series of tense/stretch/relax exercises. Responding to tension in the proper way is a physical strength. I know lots of people would disagree with me, but I often look at piano practice as a strength and habit building routine. I believe that practicing for longer periods of time is important in order to retain certain physical experiences which build into muscle memory. However, muscle memory is not the only way to play piano and so it is important to be mentally aware of what you are enforcing into your muscle memory, you have to be very focused in your practice. If you do proper things without hurting yourself, you will continue seeing results.