That would be fine except the individual who was on the 6th floor and had an unobstructed view of the SW corner saw no one.
BRW said he was back up on the sixth floor by noon, and for 10, 12, 15 minutes. Wasn't the parading dude seen at around 12:15? Seems that leaves some leeway for BRW having buggered off to join his buddies in the meantime.
I maintain that Oswald could have been doing a final check of firing positions, then hot-dogged?for himself?with the post arms thing.