Mont-Jòia recorded it with the same tune in 1976 and there's no mention of the origin of the music on the album sleeve, it just reads what I copied on my first post above.

Grishka, we didn't imagine that she could have been bluffing all the way through "de t'aver vist bèu chivalièr me costarà la vida" being just the final stroke to get rid of him while she had no intention to die at all, or at least any time soon.