I don't think he was in the tsbd building for the shooting. Reports that he managed to calmly leave the building from which he'd just fired a high powered rifle from, been seen doing this by at least one witness were told, but still evaided everyone and avoid suspicion (and the headcount) then hop on a bus, then a taxi to his lodgings,pick up a pistol to arm himself again, (so he would be in the correct area, timing wise to shoot Tippet after he just lost his cool) just seem too far fetched. Anybody driving or.riding on public transport would have reported a sighting at some point - if he was really that good, he would've handled the situation better after the fact.

He was obviously set up to take the fall, in the zapruder film you can basically see a bullet zipping in from the front, as well as numerous bystanders turning and looking towards the knoll or cowering away from it immediately