Well IF CE 399 is actually the single bullet that went thru both JFK and JC (and that's a REALLY BIG IF) then its possible for this to be a simple conspiracy that someone set up, knowing Oswald was a compulsive nut who would likely act if a VIP like the POTUS JFK could be presented as an easy target in proximity to the nuts place of work.
If LBJ is the master planner, however, he surely would not just rely on some probability of the nut acting, but would have added a few extra accomplices, like his hit man Malcom Wallace, to make sure the job gets done, should the nut, Oswald not fully act. In which case, then Oswald can be easily set up anyway, as Wallace and a 2nd shooter, using the nuts rifle, accomplish the task.
Or they just set up Oswald from the start, stole his rifle, but thats a very complicated scenario to keep Oswald free of having an alibi, so it would require Oswald kept hidden from sight between 12:17 and 12:31:30. Maybe Oswald was told during sometime that day, to meet someone in a car out back of TSBD at 12:15 if he wanted to make a quick $100. And so Oswald was in that car until just after the shots were complete, then they let him out, and Oswald the idiot went back into TSBD, via back door, and went up to the 2nd floor lunchroom to get a coke, just before Adams and Styles came down the staircase from 4th floor.
