cdunn
2nd Black Belt
Ah, I see! We're taught to try to keep our 'one point' which means to us centered over our chinkuchi. If I understand it correctly myself. We don't use a terribly low stance, but we keep our legs bent and our center of gravity under the tanden for the most part. One of our precepts is "a person's unbalance is the same as a weight."
This is all as I understand it, and I may be in error in some points, but:
The line from the your center of gravity to the floor dictates exactly where your balance is. This has some consequences: Any time your center of gravity is directly between your feet, you are extremely stable along the line between your feet. If you are on one foot, you cannot fall unless your center of gravity shifts away from overtop your foot. Mechanically, at its very most basic, a person walks by picking up his foot and shifting his center ahead of the foot that is still on the ground, so that he falls forwards onto the lifted foot. Now, it rapidly gets more complex than that, but that's the basic model.
When we keep our 'fighting stance', we keep the the center of gravity directly over the back foot. This allows a very rapid shift from the back foot to the front foot, wherever you choose to put the front foot, enabling the slip as best we can. When the center is not over a single foot, the distance and direction that you can move are constrained by the distance and direction that your center is away from a foot - because that's a portion of the movement you have to deal with first. You have to 'undo' the stability you have gained to move.