A few years back, Mr Frazier stunned folks with his story of seeing Mr Oswald a few minutes after the shooting by the Houston St. side of the Depository.
More recently, he has told of seeing a man with a rifle just after the shooting.
Let's assume for a moment these stories are not spun out of thin air but have some basis in fact................
IF the man-with-the-rifle story is true, then Mr Frazier may have been so freaked out (at what he saw + at having been eyeballed by the man) that he decided to leave immediately
IF the LHO-on-Houston story has some basis in fact, then Mr Frazier may have encountered Mr Oswald there, got talking with him, told him he was leaving------------and agreed to give his friend a ride out of downtown
These are of course big IFS, but one matter has no Ifs or Buts about it: Mr Frazier has NOT given an even halfway credible account of his post-assassination movements in the time leading up to his arrest at the hospital. This is pretty serious, as he is not just another Depository employee: he is the man who gave Mr Oswald rides to and from his place of work

Re. Mr Frazier's claimed sighting of Mr Oswald at the Houston St side of the Depository shortly after the assassination.........
Cf this from
Mr Howard Brennan:
While surveying the area, I glanced away to the side of the Depository Building and found something I could not understand. At that time there was a side entrance towards the rear of the building on Houston Street. At some point during the morning hours, the police had sealed off parking in that block and forced all cars to move. Saw horses were placed at Elm and Houston to block traffic. As I looked around I saw a lone car parked beside the Book Depository with a while male seated behind the wheel. The car was an Oldsmobile, a 1955–57 model. It is difficult to tell the exact year unless one is an expert because all those years looked nearly alike. I remember wondering why all the other cars had been made to move and this one had not.
...
One thing that interested me about the car was the way it was parked. The left front wheel was pulled sharply away from the curb and the driver had the door partially open. Later I wondered if the reason for this was so the car could make a quick U-turn in a speedy departure. As I was watching the man in the car I saw a policeman who was on foot walk over towards the car and begin talking to the man in a friendly, laughing manner. So far as I could see, there was no attempt made to get the man to move his car and after chatting for a minute or so, the policeman walked back to his post. It was this fact that made me think the police should have made some report about the presence of the car, but I have never seen any other account of this “mystery car.”
...
Many times since, especially in recent years, I have thought about the car parked alongside the Texas Book Depository and wondered where it came from and where it went. I have always wondered why the policeman allowed the car to be parked illegally beside the building with its wheels turned outward when other cars had been made to vacate the area. Of course, the paramount question in my mind was, “Who was the man sitting behind the wheel that day?”
As I watched the car, it never occurred to me that an assassination was about to take place and this might be the “get-away” car. Even though I could not have positively identified the man behind the wheel, I can say this for certain. The man was white, middle-aged and dressed in civilian clothes. I didn’t have an opportunity to study his face, so identification is impossible but I have always felt that somehow he was involved in the assassination.
Later, I would remember, “if that was a ‘get-away’ car, why didn’t it wait to pick up the killer?” Was it possible that he was being left on purpose? These questions and others tormented me for years after that experience and will never be fully answered. The one thing I knew for certain—there was a car there before the assassination and it disappeared before the assassin had time to get out of the building.
IF---------------as has often been suggested--------------Mr Oswald had been involved in what he was told would be a deliberately unsuccessful assassination attempt, and that he would be taken from the Depository in the Oldsmobile, THEN the following scenario suggests itself:
1. Mr Oswald hears the shots, is unperturbed
2. Mr Oswald, hearing Ms Gloria Calvary say JFK was actually shot, is stunned and knows immediately he's been tricked
3. Mr Oswald sticks to the agreed plan, but
there is no Oldsmobile on the Houston St side of the building4. Mr Oswald must now find an alternative mode of departure from Dealey Plaza