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

It remains true that Hosty was never asked directly about Oswald's alibi. He volunteered a statement as part of a prepared statement, but it was never subjected to cross examination. 

For instance, when he said that Oswald claimed to be in the lunch room when the President's motorcade passed the building, why wasn't he asked:

"What did Oswald say he was doing in the lunch room when the President's motorcade passed? Did he say he was eating?"

But, how could he be? Hosty said that Oswald went to lunch at noon. It doesn't take 30 minutes to finish a cheese sandwich and an apple. So, why would he still be eating at 12:30? And if he wasn't eating, what was he doing? 

An alibi consists of a location and an activity. I was at x doing y. 

When Hosty said that Oswald claimed to be in the lunch room at the time JFK passed the building he was lying. Oswald said he was Out with Bill Shelley in front. We can see him outside, and we clearly know that it is him from his anatomy, his distinctive clothing, and his bodily stance.  So, there is no doubt that Hosty was wrong, but there is also no doubt that Hosty lied because he was there when Oswald said Out with Bill Shelley in front. And he most certainly meant DURING the assassination. Shelley was not out there after the assassination by his own account. Shelley claimed not to see Oswald between 11:50 and well after 1:50 at the Dallas PD.