He doesn't know, neither do you.
How would you know if your library has Caller ID or not? You sure of that? How can you be sure of that?
I'll wait.
Because I've worked there nearly 20 years and know the phone system. How do you know whether or not YOU have Caller ID?
He didn't "gloss over" anything. He was discussing the reasons for not disclosing personal information over the phone. Why is that such a difficult concept? Do you want your credit card information released to anyone who calls the company identifying himself as an officer? Your bank records? Medical records?