I’m not understanding why they would do anything differently just because he’s the Pope. They shouldn’t have hung up on him but that’s the only customer service issue here.

Why can't they call the Vatican and confirm? You can, in fact, call (edit: and fax!) the Vatican switchboard:

https://www.vatican.va/content/vatican/en/info.html

Well, that's why it was his last-ditch effort, because it was unlikely to work.

But the reasoning is that many companies will go out of their way to help "VIPs" and may even have a separate team to handle them that has more discretion than normal front-line support staff would.

So sure, worth a shot if all else fails.

Because the pope isn’t on par with a random person. He’s like the figurehead for more than a billion people.