The problem I have with the encounter with Oswald in the Texas Theater is the way he was approached by the DPD, and specifically, McDonald.
If they believed that Oswald was the killer of Tippet, and also possilby the JFK assassin, it would seem to me they would have had guns drawn, pointing at the suspect and yelling at him to place his hands on his head and dont move BEFORE any DPD ever get close to him.