Just my opinion but I do believe Oswald did say he went Outside to "watch the P. Parade" during his 3:15 Interrogation. Oswald saying this does Not make it a fact. People/Suspects lie all the time. Oswald said he was outside the TSBD at his 3:15 Q/A BEFORE LBJ and J. Edgar came up with their LN shooter from the 6th Floor scenario.
All true!

But the Hosty notes reveal more than just a claim by Mr Oswald to have gone "outside to watch P. Parade". They also show that a confirmation of the post-shooting 2nd fl lunchroom incident with Officer Baker was
put in Mr Oswald's mouth after his death. This is as much of a smoking gun as the suppression of Mr Oswald's "P. Parade" claim, for it shows how central the lunchroom fiction became to depriving Mr Oswald of his alibi.