I found a delightful live performance from 1973 on YouTube.
And so what’s the Paleo connection? Well, it turns out that "John Barleycorn" is a personification of the cereal grain barley in this 16th century or older English folk song.
But here’s the deal: the meaning can be taken both ways. Many versions abound and in the later ones it appears to be a celebration of the barley crop; i.e., it has to die in order to provide the bread, beer, and whiskey made from it.
But not so fast. According to that Wikipedia link above, earlier versions had an opposite meaning, that "John Barleycorn" must die for all the havoc it causes.
Earlier versions resemble Burns’s only in personifying the barley, and sometimes in having the barley be foully treated or murdered by various artisans. Burns’ version, however, omits their motives. In an early seventeenth century version, the mysterious kings of Burns’s version were in fact ordinary men laid low by drink, who sought their revenge on John Barleycorn for that offense:
Sir John Barley-Corn fought in a Bowl,
who won the Victory,
Which made them all to chafe and swear,
that Barley-Corn must dye.
Another early version features John Barleycorn’s revenge on the miller:
Mault gave the Miller such a blow,
That from [h]is horse he fell full low,
He taught him his master Mault for to know
you neuer saw the like sir.
I think I’ll stick with the original meaning.