Something about Dougherty's interaction with Eddie Piper keeps bothering me. The impression I get from his testimony is that he is stood on the fifth floor, he hears a noise like a backfire coming from above then immediately goes all the way down to the fifth floor to ask Piper if he heard anything.
However, we know he doesn't come down straight away. There's not enough time for him to take the elevator down to the fifth, converse with Piper then take it back up to the sixth before Truly and Baker arrive at the elevator shaft. Truly and Baker get there approximately 40 - 50 seconds after the final shot and are there approximately 5 -15 seconds trying to get the elevator. So we know that Dougherty doesn't get in the elevator for almost one whole minute before coming down. He hears the 'noise' and then takes almost one minute, at least, before coming down.
It must be remembered Dougherty places himself working on the fifth floor when he hears the noise, the same floor as Jarman, Norman and Williams. He doesn't notice them and they don't notice him. This might be explained by Dougherty being on the west side of the building and the others being more to the east. But shortly after the shooting Jarman and co. run to the west side of the building and still they don't notice each other.
One explanation for this is if Dougherty is on the sixth floor at the time of the shooting.