Yes, I read Posner's book the year it was published, 1994. I'm a little rusty on all the arguments he brought to bear to make his case. The reason I remember the timing argument is because that's the one that most impressed me. According to Posner, Oswald not only took the job at the TBD before Kennedy had decided to go to Dallas, but he also got the job through a friend of his wife, a woman who certainly was not connected to any conspiracy.
In order to convince his readers that Johnson sponsored Oswald, McClellan must show that Johnson had plotted to press Kennedy to go to Dallas before Oswald was employed at TBD. McClellan must show that Johnson would have had good confidence that the motorcade would pass through Dealy Plaza. Johnson (or his agents) would then have told Oswald to find a sniper's perch somewhere in the plaza. The friend of Oswald's wife who asked a friend to hire Oswald, under this scenario, simply may have been an unwitting dupe who fortuitously arrived on the scene and was artfully "gamed" by Oswald.
It's a bit of a stretch, but it's not totally outside the realm of possibility.
Oswald was a nut, plain and simple. The Marines knew it, the Russians knew it, his wife knew it, the FBI and CIA knew it, the Communist Party USA knew it. They all wanted as little to do with him as possible. The various agencies covering up Oswald's contacts with them post assassination is explained by the simple fact that they didn't want to be associated with a nut who shot the president. They knew people with agendas would go ape trying to tie them to the assassination. Unfortunately, this just feeds the conspiracy theories.