So, Oswald could not have been referring to being outside with Bill Shelly before the shooting because the record shows that Shelley was one of the first outside while Oswald had not yet breached the glass door to go outside as late as 12:25. We presume that Oswald stepped outside right after Carolyn Arnold saw him at 12:25. But, that was the time of the motorcade, essentially. Within 90 seconds, after the shooting, Oswald had been accosted in the lunchroom by Roy Truly and motorcycle officer Marion Baker. Oswald could not have meant he was "out with Bill Shelly in front" after the shootingbecause Bill Shelly was not out there then. Shelly said he left immediately, with Billy Lovelady, to walk over to the railroad tracks to look around. That was before Truly and Baker even entered the building. And when Lovelady and Shelly returned, they re-entered the building through the backdoor of the TSBD, and went to the base of the back stairwell (in the northwest corner (rear) of the building). So, Bill Shelly was definitely not out in front when Oswald was leaving.
The notion that "out with Bill Shelley in front" is a reference to after the assassination when Oswald was leaving for home is really stupid. We are dealing here with the murder of the President of the United States. What the hell difference does it make who Oswald saw when he was leaving for home? Why would he need an alibi for that? Does anybody doubt that he went home? Why would Fritz say, "Lee, we want to know who you saw when you left for home because unless we get a confirmation, we're going to have to assume that you just stayed in the building." And then what? Did Oswald say, "No, I really did leave for home. You've got to believe me. Just ask Bill Shelley- he'll tell you." The point is that, just as there are no chin shadows that look anything like the vee we see on Doorman, which makes the whole shadow claim preposterous, likewise, the probative value of knowing who Oswald saw when he left for home is so useless that it is preposterous to think that it came up in the interrogation. What would Fritz want to know? He would want to know where Oswald was during the murder and whether someone could vouch for it. One needs an alibi when one is accused of a crime. One needs an alibi FOR the crime. Leaving to go home wasn't a crime- not for Oswald or anyone else. He didn't need an alibi for that.
It has been pointed out that there are contradictions in Shelley's testimony as to what he did. The best way to make sense of it is to realize that the TSBD was a CIA front company. They, the operatives of the company, were intricately involved in the assassination plot, especially as to framing Oswald. The point man on this is William Weston, and his article is entitled The Spider's Web: the TSBD and the Dallas Conspiracy. You can Google it. But, getting back to Shelley, we have his statement that he left right away for the railroad tracks with Lovelady; we have Lovelady's statement confirming it; and we have Frazier's statement that Shelley and Lovelady left right away together, but he didn't. And we have this image of Shelley and Lovelady walking to the railroad yard soon after the last shot, meaning within seconds.
So, there is no reason to doubt that Shelley did that or to put stock in any other claim he made. He was NOT out front at 12:33 or 12:34 when Oswald left for home. And Oswald was not a stupid man. He was smart enough to know that it was pointless to claim that someone saw him when he didn't since he had no arrangement with Shelley to lie for him. So, when Oswald said it, he must have believed that Shelley would confirm it. So, why didn't Shelley confirm it? Because Shelley was in on it. Shelley was a conspirator. Shelley was framing Oswald. Shelley is the one who lied- not Oswald.
And Lee had no reason to lie about that or anything. He wasn't committing a crime in leaving for home, and he did not need an alibi for it. Therefore, he must have been referring to seeing Shelley when it mattered- during the motorcade.