FWIW, I dived into the statements and testimony of Oswald's co-workers a few years back, and came to a quite different conclusion.
My discussion of this evidence is presented on patspeer.com in Chapter 4: Pinning the Tale on the Oswald.
In short, the villains here were not Oswald's co-workers, but Warren Commission Counsel Joseph Ball and David Belin, who were determined to make it look as though Oswald was the assassin, and ignore or smear anyone, e.g. Eddie Piper and Vickie Adams, who presented a problem.
As far as Dougherty, it became quite clear to me that Dougherty went upstairs AFTER the shooting, and that the one sound he heard from above was not a shot fired from far to his east on the floor above, but Truly and Baker coming down from the roof, most logically slamming the hatch door near the elevator shaft.
This, of course, was a huge problem for Ball and Belin. They needed Dougherty to be the one bringing the elevator down as Baker and Truly ran up, or else they'd have to admit there was someone who'd escaped undetected. So THEY made a point of not asking any of Dougherty's co-workers if they saw him after the shooting.
Their most egregious "oversight" was Piper. Dougherty said he talked to Piper after returning to the first floor. It would have been a simple matter, then, of asking Piper the time he spoke to Dougherty. But Ball didn't ask Piper about this on the record.
So why put the quotes on "oversight"? Because I don't believe for one second Ball "forgot" to ask Piper about Dougherty, You see, some years back I discovered within Howard Willens' memos a memo from Ball to Liebeler--who was supposed ton perform the second interview of Piper--in which Ball told Liebeler he needed to ask Piper about Dougherty. But no, instead, Ball interviewed Piper himself, and failed to, at least officially, ask Piper about Dougherty.
As Vickie Adams, among others, complained about Ball's partner Belin's habit of running through the questions off the record, and then going on the record, and asking the same questions, with the exception of those to which he'd received unsatisfactory answers, it's clear to me that Ball asked Piper about Dougherty, and received the answer he was hoping he wouldn't receive--that Piper talked to Dougherty 10 minutes or so after the shooting--and that Ball then kept this from the transcript when he went back through the questions "on the record".