The US DoD is not buying any naval ships from Italy. In fact I'm not aware of a single ship in the US Navy that was built outside of the United States.
Splitting the difference to reach the true situation:
* The US Navy contracts for shipbuilding outside of the USofA, and
* The foreign company builds for the US Navy take place at shipyards within the USofA.
eg:
“Austal’s Alabama-based shipyard is currently contracted on 11 different vessel programs for the US Navy and Coast Guard, and it is a source of pride seeing this vessel visiting our home. Plus, its Australian and historical heritage makes it all the more special.”
The U.S. Navy said on Thursday it awarded a contract worth more than $5.5 billion to Italy's Fincantieri to build its newest class of warships, known as frigates.
The contract is for detailed design and construction of the lead ship, with an option to buy nine more. If the navy exercised all options on the contract, delivery of the 10th ship would occur in the mid-2030s.
The ship will be built at Fincantieri's Marinette Marine shipyard in Marinette, Wisconsin.
The two examples given are an Italian company and an Australian company that are operating from US shipyards while remaining non US owned companies.
They do operate via US registered wholly owned subsidiaries which is a matter of bookkeeping.
In both instances the US Navy has sourced knowledge and skills from non US companies and paid them to provide service via shipyards on US soil .. with oversight from existing established home soil operations eg: Austral Marine Division in Australia.