Friends, common sense tells us that the answer to the question 'Why would the authorities go to the trouble of inventing a bus ride, and then a bus and cab ride, for Mr Oswald?' must lie in the answer to another question: 'What did Mr Oswald himself tell Captain Fritz, in that first interrogation session, about how he traveled?' For, if there was something in that answer from Mr Oswald that made the 'investigating' authorities deeply uncomfortable, then we have our motive for deception on the part of the 'investigating' authorities.
After all, these guys went to great efforts to bury Mr Oswald's claim to have visited the second-floor lunchroom for a coke BEFORE the P. Parade and then gone outside to watch the P. Parade. So it's no stretch at all that they would engage in similar shenanigans on this other phase of the 'investigation'.