Truly and Dougherty were involved in the plot. The TSBD building was part of the plot via its owner Mr Bird. Truly was conveniently ready to meet the first officers that ran to the TSBD entrance his job to confirm any assassin(s) were staff. He called up the lift shaft for the lift to be sent down but Dougherty kept it at the 5th Floor causing them to run up the stairs and taking longer to get to the 6th Floor. However, on reaching the 5th Truly and Baker got the lift but Truly took him to the roof further delaying reaching where the "shooters" were.
Oswald having seen his rifle in the TSBD earlier took it before it could be planted and hid it within the TSBD. That's why the mauser was hidden on the 6th Floor and no MC rifle initially. They found the MC after a more thorough search.
