But giving birthdate (available to anyone via a single query in a public database) and (sometimes?! - what?!) PIN over the phone wouldn't really be considered good enough here. Birthdate is, as I said, public knowledge. And a phone is too insecure a medium for transmitting a password.

I'm not super interested in an long argument about whether it's reasonable that this isn't considered secure or not. I'm just letting you know what reality looks like. And the reality is that "just call them" is not a solution, because such information will simply not be handed out over the phone.