Re: He should be proud that of that guy
Indeed. I'm always impressed by people who turn down my invitations to provide details, especially if they weren't the ones expecting a call which would ask for those.
That's solved with a simple and polite "Call me on my internal extension number so you can be sure I am legit. The sooner you call; the quicker we can get the problem fixed".
I'd rather have people over concerned about security than lax. I know who I think is the biggest "banker" here.