It's interesting that on Friday Oswald said in the hallways "I don't know what this is all about", and "they're taking me in because I lived in the Soviet Union."
At first, it seemed he was confused about getting picked up and thought the police assumed he was politically biased, and that's why he was a suspect. But on Saturday, when they started to show him "evidence", Oswald began to realize that he must have been set up - otherwise that "evidence" wouldn't exist. I think it was the backyard photos and Hidell identification because it wasn't until Saturday that Oswald was questioned about anything that he knew was fake.
Isn't it strange that as far as we know Oswald wasn't questioned about Officer Tippit, yet that's why he was supposedly arrested? They didn't even take a paraffin test until after Oswald was arraigned for Tippit's murder. He doesn't even realize that he was being brought in for the murder of Tippit, which was the reason the PD said they arrested him.
Brewer said that he saw Oswald acting suspicious just entering the theater and thought he might be responsible for Tippit's murder, which he had just learned about from the radio.
I listened to all of the KLIF, local radio broadcast from that afternoon. It was 1:45 pm that they announced JFK had died from his injuries (at 1:54:50 or the 1 hour, 54 min and 50 second, mark of the video). At no point prior to that was it announced that an officer had been shot/killed in Oak Cliff, which was the reason Brewer said he was concerned about Oswald and followed him into the theater. Maybe it was announced on a different station but I can't find it. I listened to the beginning of some others too. If it wasn't on the radio, Brewer must be lying.
Brewer is the most dubious of dubious witnesses.
Note how casually Oswald says that they are (just) taking him in because he lived in the Soviet Union. The penny had not dropped at that point, despite everything that happened at the Texas Theater.
I think that Oswald figured that they must have gotten his name off some data-list- because of his defection to the Soviet Union. And he probably thought that because he had friends in American Intelligence (at least, he thought he did) that the thing was going to get cleared up, and sooner rather than later.
Now, take a look at this which is the moments before they entered Fritz' office for the Saturday evening interrogation. There is a festive attitude in the hallways. Someone says, "There he is, Lee Oswald." And it was said like he was the guest of honor at a party. Notice how nobody, not the cops and not the reporters, show the slightest concern that he is a mad dog killer. This is where Oswald goes up to Bookhout in the hall and asks, "So, what have you got against Broby?" It is the only time that Oswald initiated a conversation with anyone. But, I also want you to notice that he walked over to Bookhout. He was doing the steering. Presumably, a detective had his arm, but that detective let him go over and talk to Bookhout.
What this tells me is that at this point, it was all chummy. And it was that evening, 5 hours later, that Oswald tried to call John Hurt in North Carolina. I have to think that he told them, "Look, I'm connected with U.S. Intelligence, and they will vouch for me. They'll tell you that I couldn't have shot anybody. I am going to contact an agent in North Carolina." Of course, they wouldn't let the call go through. And I think it played a role in the urgency to kill Oswald because what if he had reached an intelligence agent who would vouch for him? Then, the shit would have hit the fan.
But, the chumminess so evident in this video tells me that conditions were right for them to approach Oswald about participating in the ruse on Sunday. "We're going to get you out of this Lee, but we just have to call off the dogs by feigning your death. This way, they won't come gunning for you."
So, when did they set it up with Oswald? Probably on Sunday morning. At that point, he must have believed that they believed him. And I bet you that Bookhout in particular hammed it up with the friendliness and trust.
About Tippit's murder, I find it glaringly strange that we were never told Oswald's alibi for the Tippit murder. Nor were we ever told what he said about how he got to the Texas Theater. Oswald wouldn't have withheld it. Whatever he told them must have been extremely exonerating- of him.