There are serious problems with a scenario that has Dougherty going back to work after the shooting. In the scenario you are proposing Dougherty is on the fifth floor when he hears Baker and Truly coming down from the roof. This seems to be supported by Truly's recollection of seeing Dougherty collecting stock on the fifth floor as he and Baker descend to the first floor. The problem is that by the time Truly and Baker reach the first floor the situation seems quite chaotic:
Mr. TRULY. When I got back to the first floor, at first I didn't see anything except officers running around, reporters in the place. There was a regular madhouse
In your scenario, Dougherty then comes down into this 'madhouse', searches out Eddie Piper who tells him about the assassination after which Dougherty calmly returns to the elevators, presumably elbowing police officers, reporters and stunned TSBD employees aside, and returns to work on the sixth floor.
This seems highly unlikely.
He also mentions that when he finishes his lunch he wanted to see the President but there were too many people on the steps:
Mr. DOUGHERTY - Well, I would have loved to have went out and watched him but the steps were so crowded---there was no way in the world I could get out there.
This is surely a description of the steps before employees started flooding back into the building in the immediate aftermath of the shooting.
"They needed Dougherty to be the one bringing the elevator down as Baker and Truly ran up"
There is nothing to suggest the elevator came down from the fifth floor as Truly and Baker ran up and plenty to suggest it didn't. It seems more likely the missing elevator was on the sixth floor when Truly and Baker reached the fifth.
It's been awhile since I wrote that chapter, but I'm pretty sure this makes sense.
12:32 Baker and Truly look up and see the west elevator on sixth and the east on fifth. They run upstairs, seeing Oswald on the second, and then take the east elevator up to the seventh, and the ladder to the roof.
12:34 Dougherty, who was in the bath room when the shots were fired, is confused by the hubbub in the building, and goes back to work, taking the west elevator back up to the sixth. He gets some stock and goes back down to the fifth. While there he hears Baker and Truly slam the hatch to the roof as they come back down the ladder.
12:37 As Baker and Truly descend in the east elevator, Truly spots Dougherty on the fifth floor.
12:38 Dougherty follows them back down. Upon his arrival on the first floor, he goes over to Eddie Piper, who has been told to watch the back door, and asks him what has happened.
The advantages of this theory.
1. It explains why Dougherty heard but one loud sound and thought it came from above him.
2. It explains why Dougherty failed to see or hear Williams, Jarman and Norman on the fifth floor.
3. It explains why Williams, Jarman and Norman failed to see or hear Dougherty on the fifth floor.
4. It explains how Dougherty, who in the official story was standing by the west elevator for a few minutes after the shooting, failed to see or hear Oswald run down the stairs and cross the floor directly in front of him.
5. It explains why Ball never asked Dougherty if he had to call the west elevator, or if it was there on the first floor.
5. It explains why Ball failed to ask Piper when and where he saw Dougherty, and why Ball turned around and trashed Piper's credibility in the Warren Report.
6. It fits in with J.C. Price's claim he heard a loud noise minutes after the shooting.
I'm sure there's more.
The problem with this theory (for LNs):
1. It means someone descended in the west elevator just as or just after Baker and Truly ran up to the fifth floor.
