I think (maybe totally wrong on this) that part of it has to do with the conformation of your shoulds, arms, elbows, wrists and hands.
Horseyqueen is one to something here. There's no one *right* position, it does depend somewhat on rider's conformation.
Strict thumbs up, with your hand perpendicular to the ground, isn't effective for most riders either. For me, hands at a 30 degree angle, with the thumbs slightly towards each other, works best.
However, the bad news is that "piano hands" - hands rotated so palm faces down - is always a flaw. If you want consolation, it's usually a 'soft' flaw - the rider sacrifices effectiveness for softness by riding this way.
Here's an exercise for anyone with this question to try _
Get a knowledgable friend or instructor to stand on the ground and grasp your reins between the bit and your hands. Have the friend mimic the motion of the horse's head at the walk and at the canter, while you keep contact and follow the motion. Do it with your hands in the text book position. Change to piano hands and pay attention to how that changes the feel and contact.
Experiment with some other position faults - over shorten your reins and straighten your elbow. Carry your hands too high, and then too low. Have the friend continue in the same motion, pay attention to what happens to the contact and the following motion as the position changes.
Now try to apply an aid - squeeze/release your inside rein and see what happens to your feel in all the various positions
Finally, switch places - stand on the ground and "be the horse" while the friend changes hand position and pay attention to how the contact and the feel changes.
The textbook position is the textbook position because it allows for the most efficient following and feel. You can adapt that position for your own conformation (For instance, I am broad shouldered and barrel chested, so I carry my hands farther apart than the text book 4 - 6" to allow my elbow to work correctly. If I move my hands closer together, my elbow pops out and I lose efficiency.) but not to the point where you lose definitive contact.