Your thinking is fundamentally flawed. The idea of "If a spider was caught in the wild, it automatically means one of the parents was a spider" just isn't so. Just like anything else, there has to be a first. Somewhere along the way something went wrong genetically, and the first spider was hatched.
There have been no other wild spiders found. Trust me, if there had been, we would know about it. Whoever found it would have told the world, and been rich as a result. Could there still be one out there? Sure. I seriously doubt that though. It, or one of its offspring would have been found by now... and we would know about it.