It's that added middle line in the refrain, that is the interpolation I was on about!

The addded line in The New Oxford Book of Carols is the same as John Stevens' in Musica Britannica aside from OBC's having two sharps (the first mandatory, the second a suggested ficta) where MB has naturals.   The notes in OBC suggest the line has been printed for purposes of making an academic point, albeit one founded in knowledge of historic practice. Not mandatory in performance, then, but purely a suggestion by the editor(s).

I have, in fact, performed the carol several times with just two voices throughout, and I think it works splendidly in that more stark guise.