《To get a ball of malleable clay to roll down a simple path, you can force it down a specific path once, squashing it as you go. Take it to the top again, restart it from the initial starting point on the ball's surface, and it will roll down the same path.》
Not having access to the paper I would guess that the definition of "simple path" is pretty critical here. I can imagine for some paths the deformed ball reaches a point where any deformation that could move it along the desired trajectory will be evenly balanced with an alternate trajectory.
Sensitivity to initial conditions (position, velocity, ball mass) would also be a consideration I imagine.
Really "outside of the box" thinking which is refreshing.
Somehow reminds me of the white blob, "Rover" that guarded the Village in the original 1960s series "The Prisioner."