What does it matter how he got the job?   If his job was conveniently located someone could have taken advantage of that simple fact.

That being said, I do think it was Oswald's rifle that did the shooting, although I'm not totally convinced he was the trigger man.   It wouldn't have been that hard for someone to show up, use his rifle, and then slip out the building without being seen.  It's possible he knew something was going to happen and someone was going to try to kill Kennedy but didn't realize he was being set up as the fall guy.   He did say that he was only a "patsy" after they arrested him.