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.