I found the post by John Garst. I was mistaken. Garst does ask where the idea first appears of John Henry engaging in the contest in order to save his job and those of his fellow workers. But he did not say that it does not appear in the books by Johnson and Chappell. Instead, he said, "I have not found it in any of the early songs or studies." Here is a link to the thread containing the post. It's near the very end of the thread and is dated January 15, 2013.

Link to the thread containing the post

According to the "John Henry" article in wikipedia, Guy B. Johnson talked to a man named Neal Miller who said that "John Henry wanted to drive against [the steam drill]. He took a lot of pride in his work and he hated to see a machine take the work of men like him." The source cited by wikipedia is a February 2, 1930 article in the Modesto Bee and News-Herald which was written by Johnson. The article was published after Johnson's book which was published in 1929.

I don't have the article so I can't vouch for its accuracy, but I'm guessing that the quote probably is accurate. I tried to find the same quote in Johnson's book but couldn't. I did find a section in the book where Johnson discusses what Miller told him, but there is no mention of John Henry going up against the drill to stop it from taking away his job and those of his fellow workers. Possibly this is brought out in another section of the book.

One thing that has occurred to me while looking into this is that if the outcome of the contest was to determine whether or not the steam drill would replace manual laborers, an average laborer--rather than the strongest and most skilled laborer--should have been put to the test. Maybe John Henry was just an average steel driver, but his strength and steel driving skill became magnified over the years as the story of his victory circulated and turned into a legend.