A few days later I found out the call really was from the bank, and the bank had blocked my account, in a way that took a long time to unblock (don't get me started...). As ever, I found out the hard way, when I needed to use the account for something in real-time and it wasn't available.
But the call was from a different department than general customer support, the department's number wasn't known to customer service, and the account status change wasn't visible to customer service either.
So the bank's own customer service thought it was a scam call!