We had the same experience arriving at FCO from the US. Passport control glanced at our passports, but no one in our party had their passport stamped.
The slight difficulty came when we were going to return to the US. We had continued our trip by train to Switzerland and flew out of ZRH. Departure passport checks there were more thorough, with passports reviewed for arrival stamps. It wasn't a big problem, but we did each spend a couple extra minutes at the window while every page of our passport was checked and we were questioned about how we arrived without a stamp. When we explained how things were handled on arrival at FCO, one agent shook his head and commented "Not good," but we were then allowed on our way.