Oswald in the doorway: the blog of the Oswald Innocence Campaign, by Ralph Cinque

That is Hosty and Bookhout's statement to the FBI about what they heard at Oswald's first interrogation. Notice that it says that Oswald said he went home by bus. 

So, you think Hosty and Bookhout made that up, Backes? You think they put the words in Oswald's mouth? You think he said something else and they changed it to 'home by bus'? Because why would he lie about how he got home? He didn't commit any crime while going home. He didn't commit any crime, period. So, why would he lie about it?

So, you think they just made it up? But, note the date that the report was filed: November 23, 1963. Oswald was still alive. So, you think that when Oswald was still alive that Hosty and Bookhout were willing to assign other words to him than what he said, when they knew for sure that he was likely to repeat what he said to them to others? So, you think they were willing to bold-faced lie when it was certain to come back and crush them? 

That makes no sense, Backes. For their own sakes alone, they wouldn't have perjured themselves, knowing, for sure, that it would backfire.

Or, do you think they knew for sure that Oswald was going to be killed the next morning?  Well, it is preposterous to make such an assumption. You have no right to do it. And I won't let you do it. You hear me? I have told you countless times: You can't just pull stuff from out your ass. And the fact is: even if they had prior knowledge that Ruby was going to murder Oswald the next day, that still left approximately 24 hours for Oswald to tell someone else what his transit out of Dealey Plaza consisted of. And even if he didn't get around to doing that, it was still possible that something would surface about it, such as someone else coming forward, someone who saw Oswald doing it, or someone who did it with him, such as a driver who picked him up. 

In other words, if Oswald had told them that he was picked up by a private driver, and they didn't want to repeat it, they would have just left it out. They wouldn't have committed themselves in writing to telling a lie that he said he rode the bus. It wasn't worth it. It wasn't worth the risk.

Oswald told them that he rode the bus. Hosty and Bookhout said it, and Fritz wrote it down. And all that happened for one simple reason: the fact that Oswald said it.