Let's hone in on what Oswald said at the Midnight Press Conference, which may help us to understand what happened during the interrogations.
He said: "I know I am accused of murdering a policeman. I know nothing more than that."
I consider it highly significant that he referred to Tippit as "a policeman" and not by his name. It implies to me that he didn't know Tippit. Think about it. If you were talking about a guy you knew who was a policeman, would you refer to him as "a policeman"? Wouldn't you refer to him by name?
And if you listen to the way Oswald says it, it sounds like he really didn't know Tippit. He really sounded like he was talking about someone who was a stranger to him.
Now, could Oswald have been acting? It's theoretically possible but not at all likely. For one thing, he wasn't an actor, and there is no reason to think he could act that well. And with everything going on, it's hard to imagine that it would occur to him to put on an act about that.
His statement also implies that they really didn't discuss it with him because if they had, then the name "Tippit" would have been repeated enough times that he'd have gotten it into his head, and he would have referred to the man as Officer Tippit.
So, I am saying that his reference to Tippit as "a policeman" suggests that very little was said to him about the Tippit murder by anyone.
Then, a reporter asked him if he killed the President, and Oswald's response was, "nobody has said that to me yet." That sounds to me like he meant that police had not accused him, to his face, of killing the President- yet. And yet, the reporter responded by informing him that charges had been filed against him for killing Kennedy. And Oswald responded with an exasperated expression.
But, let's analyze it. Oswald said that police had NOT accused him of killing JFK. It was midnight, so he had been in custody for over 10 hours. And nobody had said anything to him about killing JFK? And they already filed charges against him for it without even asking him about it?
Again: the reporter asked him if he killed JFK, and Oswald replied that that was the first time anyone asked him that question- except for another reporter earlier in the hall.
So, what was going on in those interrogations? We have no reports of them asking him anything about the Tippit murder except for soliciting a denial from him. But, it's hard to imagine that the discussion would end there. And they had yet to accuse him- to his face- of murdering the President, even though it was being reported conclusively all over the world that he had done it?
That is weird. It is very weird. And I can't think of any reason to think that Oswald was lying about any of it.