This at least gives me pause about the LN narrative

[Michael Capasse]

The explanation is that the statement was written up by a human being and human beings make mistakes. That's not unusually when transferring something from one document to another. I can only guess as to why the mistake was made. The notes from the interviews of Baker,, Reid, and possibly others were handed to someone to write statements for Baker and Reid to sign. The person who transcribed those notes into formal statements could have simply conflated Reid's statement with what Baker said. It might be no more mundane than that or it could be something equally mundane.

Hanlon’s Razor — Never Attribute to Malice What Can Be Explained by Incompetence

No one is disputing the statement was written by someone else. 
Undocumented reasons why or how is the  you consistently make up

[Steve M. Galbraith]

One would have supposed that someone would have cleared this up long before Baker's WC testimony by clarifying with the individual who prepared the Baker and Truly affidavits. It's an oddly specific thing to gratuitously include, unlike "near the Coke machine" or something like that. Perhaps this person could have also have clarified what Baker said when he made the correction. If he immediately said, "No, you got that wrong - he wasn't holding anything," this would obviously be significant.

Baker testified on March 25, 1964. The amended affidavit (probably prepared by FBI agent Richard Burnett) that's in question was signed on September 23, 1964. So there was nothing to clarify at the time of his testimony.

My understanding was that the WC was closing up shop and rushing through affidavits to meet the schedule.

Jean Davison made this point: "Baker's affidavit of Sept 23, 1964 and a similar one from Truly were dated only one day before the Warren Report was officially released, and both their statements were, unlike all the other FBI documents I'm aware of, *handwritten*. IOW, they were prepared in a big hurry. Their statements are footnoted to a WR paragraph on the "rumor" that there was someone else in the lunchroom when Baker confronted Oswald. (Neither Baker or Truly had been specifically asked this in their testimony. Their 9/64 affidavits supplied the explicit answer: no one else was in the lunchroom.) I surmise that someone at the WC realized at the last minute that they needed a "cite" for this statement.""

David Von Pein has more details on it here: https://jfk-archives.blogspot.com/2010/07/oswald-baker-truly-and-coca-cola.html