I've never seen this but wonder if they at least used the electrical "re-creations" of certain Caruso recordings. These were done (I think) in the 1930s, long after his death anyway, and commercially issued on Victor/HMV 78s. The difference was that his voice was superimposed on a new, electrically recorded orchestral accompaniment which gave the original acoustic recordings a more modern sound. (To purist collectors, this was of course as bad as colorizing a black & white film!)
Incidentally, Caruso's silent feature
My Cousin (in which he plays a dual role) was released on
this set which I bought in the UK version some years ago, but both editions now appear to be OOP. It includes footage of Caruso performing on stage, and I once saw a UK documentary which attempted to sync part of one of his recordings of
Vesti la giubba (Pagliacci) to the film.