I think it's a mix. Yes, Pathfinder grew out of a set of house rules for improving 3.5e and that could rely on the OGL and dovetail well with their Pathfinder Adventure Path line of products (already steaming away with 3.5e material). But yes, Paizo was in a bind because of the lack of a viable 4e license and had to make a choice - either go with Pathfinder or go an indefinite period of time without a 4e-compatible product, dependent once again on a WotC license (having been burned twice so far).
They laid out their dilemma and sought the advice of participants on message boards and, despite predictions they'd come into the 4e fold, they went with PF and have had a very good run of things. Had 4e relied on OGL, that factor wouldn't have been the issue it was for Paizo. They could have had 4e-compatible materials at launch and not been in license limbo. I think that would have made the decision to go with Pathfinder a LOT harder. As it was, WotC's license fickleness only made it easier for 3PP to stick with the OGL - not just Paizo, but also Necromancer Games and Green Ronin.