Here is the link to the page that explains the George Davis claim of authorship to the original version of 16 Tons, with the lyrics. It wasn't called 21 Tons though it was called "9 to 10 tons"
I don't know when it got changed to 16 tons. But in any case, as you'll see from the book reference on the page, he didn't just tell this to the guy doing liner notes for a Folkways release years later (as someone said above), but to the author of the book "Coal Dust on the Fiddle" (George Korson) in 1959. He claimed to have written it in the 1930s which was before either Travis or Ford. The top part of the page is about the company store system, but if you scroll down a little ways you'll come to the passage from the book.
http://www.fortunecity.com/tinpan/parton/2/sixteen2.html
I think it's very likely, especially considering the fact that Travis had only 4 days to write songs before his big recording session, that he indeed would have lifted some lyrics from a song he'd heard but knew hadn't been recorded as yet, change the chords and hey presto! There is a certain amount of appropriation in songwriting it's true and especially in folk and blues. Though I haven't heard Davis's version, I understand that the Travis version as recorded by Ford is a better song.

It's also possible that when (if this is true) Travis' brother wrote him the letter containing the line "it's like in the coal mines - you get 16 tons and what do you get, another day older and deeper in debt" that he was actually quoting the earlier Davis song, in which case perhaps Merle thought it was his brother's original sentiment, if he didn't in fact remember the old Davis song. It reads like a quote because it rhymes and people don't usually rhyme in letters unless they're referencing a saying or something, you know what I mean?

As for the phrase "i owe my soul to the company store" being a phrase of Travis' coal miner father, I have also heard, and this seems probable that it was in fact a common phrase among those unfortunate to work in that industry at that time. So again, not an original line, just one used to great effect in the song.

My conclusion: I don't think Davis would have made up the story and people didn't go around suing eachother as much back then as they today, plus publishing and copyright laws weren't as tight as they are now. There are lots of reasons why he wouldn't necessarily have pursued a lawsuit to get his share of the song. Not least of which - he may not have had ironclad proof to present. After all, he hadn't recorded the song yet by the time Ford did. And finally - it's even more likely that even the Davis version was itself a folk appropriation of some even earlier tune and lyric that was going the rounds. Many times folk songs will go through a lot of successive evolution before they arrive at their final version. Nobody knew then that you could make gazillions by having your name on a tune - they just got passed around. In fact, it was the Ford recording of this tune that probably changed all that for the first time!


And finally, the Encyclopedia Brittanicca contains loads of errors. I've found some myself and contacted them and tried to get corrections made and it's like a monolith, so don't count on it being accurate!
Cheers!