I'm not clear why anyone is surprised that the FACO is in Italy. It's a simple matter of sending the Italians a spiff to keep their domestic aerospace business (Leonardo) from competing with the F-35. There is a small handful of companies in Europe that offer modern combat aircraft, notably Dassault in France and Saab in Sweden, plus the Airbus conglomerate (the former Aerospatiale, CASA, Dornier and MTU) and . Without a comfortable workshare deal, Lockheed faced Finmeccanica / Leonardo joining forces with one of those, just as they had for the Eurofighter.
If that had happened, not only might Lockheed have lost the 60-odd aircraft sale to Italy, but there was a risk that other smaller F-35 customers (particularly Netherlands, Norway, Denmark) might have gone with a European alternate.
It's also worth remembering that, jokes aside, Italy is the location of one of NATO's busiest bases, at Aviano, which (possibly not coincidentally) is the home of the USAF's 31st Fighter Wing, and the general staging base for any US aircraft flying over places south of Europe...