.. Interpol..
Yeah, no.
Interpol doesn't have field agents of their own, and can't actually go arrest people in their own name. They're not Europe's FBI or anything. It's just a name for a shared international police database, nothing else.
The cops in Italy would never, ever have said "Interpol". They would've been Italian police, acting as Italian police.
It kind of bugs me that such a basic, and rather big, error could come through so many people and apparently nobody knew this, or knew how to Google Interpols website?