Just to clarify, hydrocracking and the synthesis process to produce PAO are both catalytic processes that utilize hydrogen, heat, and pressure. And both use molecular reshapping catalysts. So it's really an over simplification to state that Group III (or even Group II) base oil is just "highly refined" crude oil. In hydrocracking/isodewaxing, the larger molecules of the feedstock are cracked and reshaped into smaller molecules, and the residual wax is isomerized, to form a base oil. And the final step is further hydrofinishing. With PAO, the smaller molecules of the feedstock are "built up" and shaped to form a base oil. And the final step is further hydrofinishing.
As I pointed out in another thread, in the early days of gasoline production, when demand began to rise with the advent of cars powered by internal combustion, the oil companies had to develop a new way to produce gasoline since the amount produced naturally through distillation wasn't enough. What they came up with was "cracking" the larger crude molecules to produce gasoline. This "cracked" gas was commonly referred to at the time as "synthetic gasoline" and was universally lauded for its superior properties, including a much higher octane than "natural gasoline."
Hydrocracking involves the restructuring of the feedstock molecules to the point that they don't resemble their original state at all. It would seem, then, that the final product of hydrocraking can lay claim to being "synthetic"—at least in some sense of the word.