Wow, thank you for the very thorough response. I'm thinking Reuben's Train has passed by a couple of times during this involved discussion, we better not miss the next passing. Chooo chooooo!
Yes, 'public domain' means 'not (or no longer) under copyright.' https://en.wikipedia.org/wiki/Public_domain
So you can freely record it. As per the same link, it seems the PD designation can be complicated, eg not strictly determined by age. The closest thing to a simple rule is this: "Musical compositions fall under the same general rules as other works, and anything published before 1925 is considered public domain."
So, how to possibly find the first publishing date???
Though fiddlers' versions of tunes can be challenging to learn from, a GREAT source of information about a tune's history is the Traditional Tunes Archive ( https://tunearch.org/wiki/TTA ), formerly known as Fiddler's Companion ( http://www.ibiblio.org/fiddlers/ ), which seems to still be functional.
Using this, it's still not clear when 'Rubin' was first published: http://www.ibiblio.org/fiddlers/REE_RH.htm#REUBAN('S_TRAIN)
However the entry says a 1927 recording, Train Forty-Five, was "derived from" Ruben's Train, implying R's Train is at least somewhat older. Note that this source call's it "Reuban's Train" or "Old Reuban." (More "folk process" in action!)
In any case, if I recorded it, I'd just assume it's in the public domain and not lose a minute of sleep over it.
By the way, that reference calls it a one-part tune. (" Old‑Time, Song and Breakdown. USA, North Carolina. D Major/Mixolydian. One part." )
So perhaps that bluegrass version reflects this, while other versions evolved a distinct "second part," which I agree makes for a more varied and interesting sounding piece of music.