So what another country says about who is or is not a citizen is completely irrelevant. Some here don’t agree.
Those people are wrong. Only US law determines the status of US Citizens. Italy is not the only country that provides citizenship to the descendents of their former citizens. Ireland does it too, and I believe Israel does as well.
But the US only recognizes US law in deciding who is or who is not a US Citizen. The fact that other nations allow a claim of citizenship is irrelevant.