I think nearly all the ATM machines in Italy are in the same network. I have not paid fees on cash withdrawals. I mostly use an HSBC Premier Debit card and HSBC does not add a foreign exchange fee.
I did run into one ATM at an Airport which offered to do the foreign conversion at their end, "saving you your banks fees". The exchange rate was dreadful. But I was able to decline the offer and withdraw as usual.
My wife is always baffled why there are still money exchange businesses - can't imagine who would use them or why.