Oswald in the doorway: the blog of the Oswald Innocence Campaign, by Ralph Cinque

Let's look at this testimony of Bonnie Ray Williams. He said that after the shooting, they saw the throng of people, including police, herding towards the railway area, so they "followed" them by moving westward on the 5th floor to the west windows, so they could watch. And they were still there when the first policeman arrived, whom they recognized as a motorcycle cop from his helmet. Then, they went down to the 4th floor, where they saw two women at a window. We'll pick it up from there:

Mr. BALL. After you stood at the west window for a while, what did you do?
Mr. WILLIAMS. After we stood at the west window for a while, we decided to go down. Then we left.
Mr. BALL. How did you go down?
Mr. WILLIAMS. By stairs.
Mr. BALL. Where did you go?
Mr. WILLIAMS. We went to the fourth floor first. Then we paused for a minute there, where we saw these women looking out of the window. Then we decided to go down to the first floor, and we ran on down.
Mr. BALL. When you got to the first floor, what did you see there?
Mr. McCLOY. How did you get to the first floor?
Mr. WILLIAMS. By stairs.
Mr. DULLES. There were some people on the fourth floor?
Mr. WILLIAMS. Yes, sir. I remember seeing maybe two or three women standing in the window, looking out the window.
Mr. DULLES. Looking out the window?
Mr. WILLIAMS. Yes, sir.
Mr. McCLOY. Which stairway did they take, west or east?
Mr. BALL. There was only one stairway, and that is the one in the corner. Did you run down stairs?
Mr. WILLIAMS. Yes, sir; we ran.
Mr. BALL. When you got to the first floor, what did you see?
Mr. WILLIAMS. When we arrived to the first floor, the first thing I noticed was that the policemen had rushed in. I think some firemen came in with a water hose. And then the next thing that happened, these detectives, or maybe FBI--anyway, they stopped us all and they said, "Do you work here?" And we told them yes. And they took our name, address, and they searched everybody. And then the other fellow--I think one fellow asked whether we had been working upstairs. I think we told him yes. They got out all the fellows I think that was working on the sixth floor at the time, and they took us all down to the courthouse, I think, and we had to fill out some affidavits and things.
Mr. BALL. You made out an affidavit there?
Mr. WILLIAMS. Yes, sir.
Mr. BALL. Did you go out of the building shortly after you came downstairs?
Mr. WILLIAMS. They wouldn't let anybody out of the building. 
Mr. BALL. How long after you came down from the first floor were you taken over to the Police Department?
Mr. WILLIAMS. I couldn't give you the exact time, but it wasn't long.
Mr. BALL. You can't give me any estimate in minutes?
Mr. WILLIAMS. No, sir; I would not want to say.
Mr. DULLES. Did you see Lee Oswald at any time during this period?
Mr. WILLIAMS. No, sir; I don't remember seeing him.
Mr. BALL. Were the police with you?
Mr. WILLIAMS. Yes; they were.
Mr. BALL. Were your two friends with you, Jarman and--
Mr. WILLIAMS. No; they wasn't with me. First I think they took me and another fellow, Danny-- they took us in one car. Then they took some other fellows in another car, and then another car, I think.
Mr. BALL. You were with Danny Arce and one or two police officers?
Mr. WILLIAMS. Yes, sir.

So, there is Bonnie Ray Williams and Danny Arce waiting to get in the police car. But, how does that allow for Bonnie Ray to be milling around outside the TSBD 15 minutes after the shooting? What grounds are there to extrapolate that from his testimony? I don't see that there are any. When asked if he went outside, he said that police weren't letting anyone out. The implication seems to be that he didn't go out until it was time for them to be taken to City Hall.