That's an accident of the trajectory chosen for the animation. The system doesn't have a kinematic singularity from input to output, just from output to input. Instead it has a zero from input to output, which is why it needs an otherwise redundant motor.
To elaborate, there's one point where spinning an input motor doesn't rotate the output. When they reverse-generated the input trajectory from the output trajectory, that point has no unique solution; spinning the input motor has no effect on the output so the input can do whatever it wants. The animator let the input do a sudden backflip, but it didn't have to; that motion was not required and had no effect. It was probably just the output of a matlab script or something.
To elaborate, there's one point where spinning an input motor doesn't rotate the output. When they reverse-generated the input trajectory from the output trajectory, that point has no unique solution; spinning the input motor has no effect on the output so the input can do whatever it wants. The animator let the input do a sudden backflip, but it didn't have to; that motion was not required and had no effect. It was probably just the output of a matlab script or something.