This is one of the related reasons why I finally got my ducks in a row and switched away from Chase three years ago. Their potential-fraud-has-happened outreach department was, in my experience, terrible about this. It didn't help that their potential-fraud-detection department was similarly bad. ("You used your debit card at an AM/PM in Washington State!!!!" Yes, I know, it is about 900 feet from my house; I go there regularly.)
Point being, I got quite a few calls from their (real) fraud prevention department about (supposed) fraud. Each time, the rep who called me would get mad at me for not handing over the last four of my SSN and my complete address to the calling party. I pointed out, each time, that they were the ones who called me so I should be verifying them. "But, sir, WE are the bank and you could be anyone who just answered your phone."
The credit union I now use just presents a message with their name and a request to call back. "We may have detected a fraudulent purchase; please give us a call at the number on the back of your card and reference case number [digits]." Fortunately, their system is much better; I've only heard this message once.