This is the full story I was just told, when I asked...
It was Val Forgett who supplied the Italians with the original "Remington" to be used as the model for a Remington replica. Due to the poorer levels of research and knowledge back in the late 1950's and early 1960's, what Val sent them to copy was not a Remington New Model (1863) but rather a Transitional Remington. Remington had been producing the Elliot patent version (aka "M1861") revolver, when Sam Remington made a number of changes that the factory implemented piecemeal late winter early spring of 1863. One of the "Elliot" features not yet changed on Forgett's sample was the exposed barrel threads. Remington also changed the radius of the grip on the New Model which for many shooters crimps the knuckles. After a couple decades or so, the Italians corrected the barrel threads so one finds the older early production with no exposed threads, half, and a quarter before switching over to the standard exposed threads of the true M1863 New Models.