If you're in Italy and a citizen of Italy, you are covered. There are likely gray areas for non-Italian citizens. They generally see you first, and ask questions later though, especially if you have the health service card, which any Italian would. I (US citizen) went to the emergency room once before getting mine, and the bill was €0.00, although I did have to buy some stuff at the pharmacy and was charged full price for it, for which the pharmacist was quite apologetic.