However, typically you surrender your passport to the front desk when you check into a hotel. Even with an Air B&B they asked for our passports when we rented apartments. So, typically if you are just walking around the city and you are stopped you just tell them that the hotel has it. They may walk/drive back to the hotel and ask the management to confirm your ID.
Our mistake was we should have brought them on the train.
Our Italian friend told us that the policeman could have taken us to the local station and held us there. Then my wife would have had to go back to Florence and get our IDs and then return. They were in the safe in the room.
FYI, my son and I both had purchased ID holders that we wore under our clothes. We also both purchased money belts. I had four 100 Euro notes in mine. He had about the same.
We were in technically wrong. I just think the policeman was being a dink. At first he did not want to accept my wife's NH drivers license too. Even though it is a real ID. He did and fined both my son and ID for not carrying ID.
Lesson learned.
Another expensive lesson happened in Positono on the Amalfi coast. Never order in a restaurant on the waterfront without looking at the menu first. That cost me almost as much as the train cop. My wife order a half dozen oysters and a cappachino. I ordered a Lemoncello spritzer. The oysters
were 14 EU a piece. The spritzer was 26EU. Exchange rate was
about 10%. So, in the first minute of sitting down we spent about $132 US.