I think it's quite likely that, as Jim suggests, ballad singers have always varied the lyrics a bit. There are a lot of set phrases that will carry certain parts of a story along:
"He took her by the lily-white hand" or "middle so small"
"Arise and tell to me..."
"And up then spoke.."
"Arise and let me in"
"and woe betide..."
"This pretty girl grew thick around the waist"
"Go saddle to me the milk-white steed"
"I wish my baby it were born"

and so on.

These would be of little use to a lazy singer who had never learned the songs in the first place, but an experienced singer would be able to draw on them to hold the story together when there was a memory lapse.

I'm not sure I'd dare attempt that. I might accidentally launch into a completely different song and find myself unable to get the story back on track. But I admit I have occasionally made up a line or a half-line as I went along, rather than stop and think about it.

Marje