In the UK the first three cases in a year are free, but from the fourth onward the bank has to pay £750 [1]. It doesn't matter the outcome is - the customer could be totally innocent or the next Bernie Madoff - the bank has to pay. A customer saying "I will get the Ombudsman involved" is heard by the bank as "if we don't make this go away right now, we will get charged £750 (plus any compensation the Ombudsman may award)". It does tend to make them sit up and take notice, I hear, presumably because banks get a lot of complaints and so a large bill.

[1]: https://www.financial-ombudsman.org.uk/businesses/resolving-...