Wow. DCAGUY, thank you so much for clarifying this. After further review, you are right. I stand corrected.
The source of my initial info was when I called Bank of America, the issuer of my card and the lady told me coverage applies for the USA only. She was the third person I'd been transferred to in order to get the question answered, so I trusted that she knew what she was talking about.
I just called Visa Travel Assist at the phone number on the web link you provided and, sure enough, I have coverage in Italy with Visa.
Still no coverage, though, with American Express Platinum, the benefits for which I pay 10x per year compared to the Platinum Visa. I would normally say that's puzzling, but I'll just add it to my growing list of frustrations with AMEX.
Thank you again!!