The bogus item here is the idea that the building was "locked down" at 12:36.
Harkness' 12:36 transmission reads: "I have a witness that says came from the fifth floor of the Texas Depository bookstore at Houston and Elm. I have him with me now. We're going to seal off the building." That is, Harkness expresses the intent do lock down the building, and he hasn't begun to do it yet.
At the time Harkness made this transmission, he's at the west end of Old Elm, past the pergola, having just run into Amos Euins. He put Euins on the back of his trike, and drove him to the front of the TSBD. The Martin film shows Harkness trundling back to the TSBD with Euins on the back of his ride....while Inspector Sawyer's car pulls to the curb in the background. Sawyer, then, doesn't arrive at the TSBD until 12:36 at the earliest.
Once out of the car, Sawyer gets update on the situation by the officers there, then goes into the TSBD with them into the building. Sawyer's group takes the front elevator up to the 4th floor and looks around, running into Truly as he's on his way down from the roof. Seeing nothing incriminating on the fourth floor, Sawyer's group then takes the elevator back down to the first floor, then leave the building. This is the point in time where Sawyer says he stationed two officers at the front door with orders to no let anyone in or out.
Sawyer thought that three minutes elapsed from the time he got out of his car until he returned outside from the fourth floor expedition. So if arrives no earlier than 12:36, then the front door guard is posted no sooner than 12:39. I should point out that Sawyer's group spent enough time on the fourth floor that they made it back to a point near the back stairs for Truly to have seen them. Between 12:41 and 12:43 (and probably closer to 12:43 than 12:41) Sawyer makes his first broadcast of the afternoon, asking that more officers be sent to the TSBD. So Sawyer has to have returned from the 4th floor by then.
The upshot is that there were no officers guarding the front door until at least 12:39, and maybe not until after 12:40. Perhaps as late as 12:43.
What makes you think that Sawyer did not leave a man behind at the front door when he entered the building?
12:36 Channel 1 260 (Sgt. D.V. Harkness) Witness says shots came from fifth floor, Texas Book Depository Store and Houston and Elm. I have him with me now and we are sealing off the building.
12:37 Channel 2 137 (Patrolman E.D. Brewer) We have a man here who says he saw him pull the weapon back through the window off of the second floor from the southeast corner of that depository building
Dispatcher All right, do you have the building covered off?
137 No, about 3/4 of a block away from there.
Dispatcher All right, pull on down there.
Brewer was 3/4 of block away from the TSBD and went down there to lock down the building.
And Sawyer also testified;
Mr. SAWYER. Well, I didn't see anything that was out of the ordinary, so
I immediately came back downstairs to check the security on the building.Mr. BELIN. When you say check the security on the building, what do you mean by that?
Mr. SAWYER. Well,
to be sure it was covered off properly, and then posted two men on the front entrance with instructions not to let anyone in or out.
Mr. BELIN. What about the rear entrance?
Mr. SAWYER. We'll, I also had the sergeant go around and check to be sure that all of those were covered, although he told me that they were already covered.
Mr. BELIN. When was the order given to cover the front entrance of the building?
Mr. SAWYER.
Well, they had it covered when I got there. There were officers all around the front. The only thing I don't think had been done by the time I got there, was the instructions not to let anybody in or out.
You kinda left out the parts in bold. I can only wonder why.
Oh btw, Styles was photographed standing next to Sawyer's car and she entered the building before it was locked down. Adams tried to follow her a couple of minutes later and was stopped.