According to me, bank or any other employer must respect his employees. Employee has a problem - try to help or at least find out what could be done to help. I dont know what should exactly bank do. Maybe send this guy to visit a psychologist first. Or it leads to: addicted employee - fire immediately, employee got sick - fire him, employee urgently needs to pick up a child from school or child got into accident - fire employee, employee spend 1:01h instead of 1h lunch - fire.
It greatly depends on what company you are working, and they policies when comes to mental health and management of their employees. There are companies which have their own psychologist and department dedicated for employees to seek mental well-being, all sponsored by the company itself. On the other hand, there are companies which work at the edge of the law and offer their workers the bare minimum for the company not to break laws of the country and get fired, the latter case is specially prevalent in countries which are not developed and where man-of-war is not as valuable as in other places, where people can be replaced easily with no consequences.
Here in my country I have seen people getting fired for the most absurd things, because the market is saturated and the economy is bad, so businesses can mistreat people working for them.
Wherever that bank was from, it is clear there was no within the scope of law to provide psychological attention to their employees, otherwise she would have not been fired immediately in the manner she was.
It is just a manner of fact that companies reserve their right to fire people to work for them with little to no excuse, and that is something we must live with, at least until there are changes of laws.