Thats not quite right - PF as much originated in 4e existing at all, as 3.x was promised to be the definitive system you could use forever (admittedly this was never going to be true) and 4e dropped the OGL, so Paizo, which includes some of the original OGL writers and 3.x designers, could no longer produce materials for it.
It was only when they were designing 2e that they looked at 4e and decided they could do better, taking many of the underlying mechanics and combining them with 3.x's range of choice.