Posner's argument hinges on the timing of Oswald's employment at the Texas Book Depository. He proved that the itinerary of the motorcade could not have been known to Oswald prior to his taking the job. Neither the decision to go to Dallas nor the itinerary had been decided upon in the WH until after Oswald had aready started working in the book depository. Ipso facto, according to Posner, it was sheer dumb luck that gave Oswald access to a sniper's perch on the day Kennedy came through Dallas.
Now here's the twist. Posner's theory assumes that WH officials had clean hands. He writes only about the public disclosure of the decision to go to Dallas. For Posner it is the date of the public disclosure that forecloses the possibility that Oswald could have known to get a job at the TBD. But if high level officials in the WH knew a good deal earlier of Kennedy's intention to go to Dallas, and the decision was simply held to a small circle for a period of time, then Posner's theory falls apart. And if one of those officials was Lyndon Baines Johnson, then McClennan's theory is not disposed of by Posner, and Johnson conceivably could have plotted to put a sniper at that spot on that day.