No I do not believe that is true but I also not not believe the numbers in other countries. 

They all count differently and kind of weird is people are diagnosed with it although tests are not done. Also if you stay home sick nobody knows. I know from people who are labelled with it although they never saw a doctor and suffer over years from something else.

I read the numbers of people died in one other European country (low) and all those people suffer from heart diseases, high blood pressure, are diabetic, have cancer, etc illnesses that would make them die soon anyway. There was one alcoholic with liver and pancreas problems. 

I do believe in a natural immunity though.
What we know so far is there's more as one Coronavirus we have to deal with. 
In Austria it started with two different types, in Hungary they said they found several kinds and all needed to be found to make the right vaccine. 
Might be you only have one type, might be you are more immune, might be the virus became weaker before it mutated, might be in Italy a different variant is spread on purpose because that is what I believe. This is man-made, set out on purpose, different variants are used and the world's leaders knew about it. In October 2019 they discussed how to act during a pandemic. They had a very good reason for that. 

If your restaurants were open for that long I wonder why they were suddenly closed. That doesn't make sense. 

With us restaurants can keep working you just need to pick it up or they deliver it at home. This means it only saves them money.
Supermarkets, drug stores make big money and people seem to buy a lot extra online these days (I did not). 
It's only a month most countries have a lockdown which I consider as a very short period.