If Oswald Was The Assassin, Did He Plan His Escape From The TSBD Very Well?

[Alan Ford]

This is not Oswald's claim. It's Fritz's claim.

Incorrect, Mr O'Meara!

[Thomas Graves]

Incorrect, Mr O'Meara!

Dear Alan,

Have you recently found a tape recording of the interrogation session at issue?

--  MWT 

[Dan O'meara]

Incorrect, Mr O'Meara!

Well that settles that 

[Dan O'meara]

When considering the potential escape route of the assassin (assuming its not Oswald) I keep getting drawn back to the fifth floor magical, mystery missing elevator. When Truly and Baker reach the elevators and look up they see both elevators up around the fifth floor but by the time they get up to the fifth floor (3 minutes later?) the west elevator is gone. What happened to it?
Jack Dougherty testifies that after he heard the shots whilst on the fifth floor he takes the elevator down to the first floor for his, slightly bizarre, encounter with Eddie Piper. He takes the elevator all the way down to the first floor, walks the entire length of the building to ask Piper if he heard anything. When Piper confirms he heard the shots Dougherty turns around and takes the elevator up to the sixth floor. Piper doesn't mention this encounter in his WC testimony even though he is specifically asked "And the first people that you saw on the floor after the shooting was who?" The slightly odd thing is that no-one noticed the elevator being used - not Truly and Baker on their way up or Dorothy Garner on the fourth floor.
By the time Truly and Baker have finished on the roof and are on their way down Truly sees Dougherty on the fifth floor. Could the assassin simply have taken the elevator down to the first floor and left by either the Houston Street dock exit or the door on the west side of the building.

[John Iacoletti]

He takes the elevator all the way down to the first floor, walks the entire length of the building to ask Piper if he heard anything.

Why do you think Piper was an entire length of the building away from the elevators?

[Dan O'meara]

As I understand it Piper was at the windows at the front of the building. In his affidavit the day after the assassination he states:

"I went to the front window on the first floor and ate my lunch and waited to see the President's parade go by. I saw the President pass and heard some shots..."

With the elevators being on the far north wall and the front windows on the far south Dougherty walks the complete length of the building (assuming Piper was still in the same area shortly after the shots).
I just find it really strange Dougherty would think to go all the way down and across to see Piper, who told him he heard shots and then go back up to the sixth floor, especially when he states in his WC testimony that he heard the noise when he was on the fifth floor and thought it came from above. He went up to the sixth knowing there had been shots coming from that area. Doesn't smell right.

[John Iacoletti]

Mr. BALL. And were you sitting there when you heard the shot?
Mr. PIPER. That’s right.
Mr. BALL. Tell me what you heard?
Mr. PIPER. I heard one shot, and then the next shot went off-the one that shot him and I got on up and went on back, back where they make coffee at the end of the counter where I could see what happened and before I could get there, the third shot went off, and I seen the people all running and in a few minutes someone came in the building, and I looked up and it was the bossman and a policeman or someone.
Mr. BALL. You say you heard one shot-you heard two shots and you got up and then what happened, where did you go?
Mr. PIPER. I came out to the end of the counter where they make coffee there by the stand.

I'm not totally sure though where this counter was where they make coffee.