Sorry for reviving this thread, but I happen to be Italian, so maybe I can give a more detailed inside view. I don't know if Italy has had a concertina tradition in the past, but certainly there is not a scene now. The presence of concertina makers here is actually a mystery to me, being an instrument with apparently no players and tradition. The only tutor in italian I found (a very basic introduction to the anglo concertina found on the net) asserts that "the anglo concertina is an instrument that fits particularly well to italian traditional music - and even if it cannot be considered a typical instrument within the circle of italian traditional music, some players have been reported which probably had it learned and imported after a working experience abroad".
In fact, Italians mostly play accordions, a very few play bandoneons (tango players), but no concertinas. I know of one which actually owns one, but actually plays bandoneon instead, and most of the non-playing people don't even know what a concertina is. I recently bought an english concertina and, while I'm still learning the basics, friends keep asking me what it is and they call it something like "that little accordion".
So, everything makes me think that we have no tradition in concertina, despite the fact the we make them! Not saying that there are no players, but certainly not enough to become a tradition, at least in my part of Italy.
Maybe in southern Italy, where the musical tradition is much stronger, there are more players and a different situation.