It's important to distinguish between the described technique of the walk - presented with ZERO rise and fall, and the more common in dancing situation of a walk taken with rise or fall.

With a flat walk, to lower the heel with the feet apart would be to allow the body to surge backwards. As we know a flat walk is also a constant-velocity walk, perfectly smooth floating with no surging or pulsing. The rolling of the feet cannot be allowed to get ahead of the progress of the body.

In a lowering walk though the heel needs to lower before the foot closes, because the main lowering of the body in a downswing as the feet are closing is the flex of the knee, and of course in ordinary situations we do not lower from the knee until the foot is already flat on the ground.