In the original Jeremy isn't even a collier but a farmer, and I get the impression that Nichol's quip about brigadier or grenadier is said to tease her, not out of any ignorance of the difference, on his part at least.
I never quite liked it when I first heard the song, but having found the original I sort of combined the two and put it in my book - it is such a temptation to keep adding more songs when there are still blank pages.