When I first read Tiger's comment that Johnny Cash sings the word Minnesota "kinda parenthetically," I took it to be facetious, but on re-reading the lyrics, I can see exactly why he put the word in parentheses.

It calls attention to the fact that the rhyming word in that line is "St. Paul." It rhymes with "drawl" in the next line.

Cash repeats the pattern in the next verse. "Later on" rhymes with "she's gone"—and so Tiger puts the words "down the river" in parentheses for the same reason.

Also notice that "Minnesota" exactly matches the rhythm of "down the river" although it doesn't quite match "southern drawl" or "boy, she's gone," which is what you might expect.

Brilliant. It's a very unusual and intricately planned metrical/rhyming structure by Cash, and an unusual but appropriate way to notate it by Tiger.

This analysis might seem kinda far-fetched if you only read the lyrics, but I think it will become clearer if you listen to it. There's a video at YouTube of a TV appearance by a very young-looking Johnny Cash.