> Tell them you need to verify them, and then ask how they propose you do that.
Last time I did that, the caller said "but you can just trust that I'm from <X>." So I replied that they, likewise, could just trust that I'm me, and you could practically hear the light bulb click on. They did their best to help from there but their inbound lines aren't staffed effectively so my patience ran out before I reached an operator.
I can't remember which company it was, but I got a call a few years ago about some issue with an account, and they wanted some information to "verify my identity"
I said wait a minute, you called me. Shouldn't I be verifying who you are?
The guy kind of laughed and said yeah, but this is the process I've been given to follow. I said I would call back on public customer service number and he said that would be fine.
It turned out it was a legit call, but just weird that they would operate that way.
I wish I could remember who it was. A credit card, I think.
This happened to me with AT&T herein Mexico: I have an AT&T pre-paid sim card that expires after a year. At the end of the year I got a call supposedly from someone form AT&T and told me about some special discount offer if I pre-paid for another year. The catch is that I needed to pay over there by phone ... (give my card details).
I told her that I preferred to call the AT&T number and for her to tell me what options should I press to get to her. She couldn't give me an answer to that.
What's fun here is, the moment they ask you for anything, flip the script and start to try to establish a trust identity for the caller.
Tell them you need to verify them, and then ask how they propose you do that.
Choose your own adventure from there.